GTCO 2011 - Workshop on Graph Theory
and Combinatorial Optimization
Shanghai·China
October 29- 31, 2011
Sponsored by
Department of Mathematics, Shanghai University
Open Laboratory for Operations Research & Optimization
Shanghai Operations Research Society
Supported by
The Key Disciplines of Shanghai Municipality-Operations
Research and Cybernetics
GTCO 2011 - Workshop on Graph Theory
and Combinatorial Optimization
Workshop Organising Committee:
Chairman: Qingwen Wang (Shanghai University)
Co-Chair: Liying Kang (Shanghai University)
Members: Yanqin Bai (Shanghai University)
Xiaomei Jia (Shanghai University), Erfang Shan (Shanghai University)
Xiying Yuan (Shanghai University), Weiya Zhong (Shanghai University)
Xiaoxia Wang (Shanghai University)
Wenhuan Wang (Shanghai University)
Prabhu Manyem (Shanghai University)
Yongjian Yang (Shanghai University)
Xiwen Lu (East China University of Science and Technology & Shanghai
Operational Research Society)
Zhaohui Liu (East China University of Science and Technology &
Shanghai Operational Research Society)
Organizers:
Department of Mathematics, Shanghai University
Shanghai Operations Research Society
Website:
http://math.shu.edu.cn/teacher/prabhumanyem/gtco2011/index.htm
2
Programme of
GTCO 2011 - Workshop on Graph Theory and Combinatorial
Optimization
October 29- 31, 2011
Shanghai University
October 29, 2011 (Saturday)
Time
7:00---8:00
8:30---9:00
9:00---9:10
Place: Lecture Hall of Lehu Building 乐乎新楼报告厅
Breakfast: Dining Room of Lehu Building 乐乎新楼餐厅
Opening Ceremony
Photo
I
October 29, 2011 (Saturday)
Plenary Talk
Time
9:10---10:00
Place: Lecture Hall of Lehu Building 乐乎新楼报告厅
Speaker/Title
Nick Wormald
University of Waterloo, Canada
Chairman
Yusheng Li
Cops and Robber on a Random Graph
10:00---10:20
10:20---11:10
Tea Break
Ding-Zhu Du
University of Texas at Dallas, USA
Routing Cost Constrained Connected Dominating Sets
11:10--12:00
Xuding Zhu
Zhejiang Normal University
Some Problems on Circular Colouring of Graphs
12:00-13:30
Lunch: Dining Room of Lehu Building 乐乎新楼餐厅
II
Xiaodong Hu
October 29, 2011 (Saturday)
Section Talk
Time
13:30---14:00
Section Talk A: Lecture Hall of Lehu Building 乐乎新楼报告厅
Speaker/Title
Chairman
Xiaodong Hu
Academy of Mathematics and Systems Science,
Chinese Academy of Sciences
Section Talk B: Room 507, Building G
Speaker/Title
Chairman
Guochuan Zhang
Zhejiang University
Approximation Algorithms for a Bi-level Knapsack
Problem
Improving Performances of Selfish Ring Routing via
Limited Cooperations
Yusheng Li
Tongji University
Guochun Tang
Shanghai Second Polytechnic University
Remarks for the Local Lemma
A Revised Proof of the Optimality for the
Kise–Ibaraki–Mine Algorithm
14:00---14:30
An Chang
Jianliang Wu
Shandong University
Zhiyi Tan
Zhejiang University
Total Coloring of Planar Graphs Without Intersecting
Short Cycles
Scheduling with Machine Maintenance for Minsum
Criteria
Weifan Wang
Zhejiang Normal University
Hong Zhu
East China Normal University
The Surviving Rate of a Planar Graph
Arithmetic Operations Over Regular Languages
14:30---15:00
15:00---15:30
III
Xiwen Lu
October 29, 2011 (Saturday)
Section Talk
15:30--15:50
Time
Tea Break
Section Talk A: Lecture Hall of Lehu Building 乐乎新楼报告厅
Speaker/Title
Chairman
Section Talk B: Room 507, Building G
Speaker/Title
Liming Xiong
Xujin Chen
Beijing Institute of Technology
Academy of Mathematics and Systems Science,
Chinese Academy of Sciences
15:50---16:20
An Extension of the Chvάtal-Erdös Theorem: Counting
the Number of Maximum Independent Sets
Bonds with Parity Cons Traints
Zhiquan Hu
Xiaoguang Bao
Jianliang Wu
Central China Normal University
East China University of Science and Technology
16:20---16:50
16:50---17:20
A Lower Bound of Circumferences Involving
Connectivities and Independence Numbers of
Subgraphs
Improved Approximation Algorithms for the
Yuehua Bu
Kejun Zhao
College of Mathematics Physics and Information
Technology, Zhejiang Normal University
East China University of Science and Technology
Clustered Traveling Salesman Problem
Fully Polynomial Approximation Schemes for
Two-agent Scheduling on Parallel Machines
BB-coloring of Planar Graphs
18:00
Chairman
Banquet: Xuanleshi Hotel 轩乐诗大酒店
IV
Weiya Zhong
October 30, 2011 (Sunday)
Plenary Talk
Time
Place: Lecture Hall of Lehu Building 乐乎新楼报告厅
7:00---8:00
Breakfast: Dining Room of Lehu Building 乐乎新楼餐厅
Speaker/Title
8:30---9:20
Chairman
Zhicheng Gao
University of Macao & Carleton University
Asymptotic Properties of Locally Restricted Compositions
Weifan Wang
9:20---10:10
Beifang Chen
HongKong University of Science and Technology
Tutte Type Polynomials From Viewpoint of Homology and Cohomology
10:10---10:30
Tea Break
V
October 30, 2011 (Sunday)
Section Talk
Place: Lecture Hall of Lehu Building 乐乎新楼报告厅
Time
10:30---11:00
11:00---11:30
11:30---12:00
Speaker/Title
Michel Habib
University Paris Diderot - Paris7, France
Algorithms for Some H -join Decompositions of Graphs
Yaokun Wu
Shanghai Jiao Tong University
A 4 -sweep LBFS Certifying Algorithm for Recognizing Interval Graphs
Min Xu
Beijing Normal University
On the Restricted Forwarding Index Problem in Communication Networks
12:00---13:30
Chairman
Lunch: Dining Room of Lehu Building 乐乎新楼餐厅
VI
Lianzhu Zhang
October 30, 2011 (Sunday)
Plenary Talk
Time
13:30---14:20
Place: Room 507, Building G
Speaker/Title
Sanming Zhou
University of Melbourne, Australia
Chairman
Changhong Lu
Symmetric Graphs and Transitive Block Designs
Section Talk
Place: Room 507, Building G
Time
14:20---14:50
14:50---15:20
Speaker/Title
Chairman
Jiming Guo
China University of Petroleum
On the Laplacian Spectral Radius of Graphs
Changhong Lu
East China Normal University
Huiqing Liu
Identifying Codes and Locating-dominating Sets on Paths and Cycles
15:20--15:40
Tea Break
VII
October 30, 2011 (Sunday)
Section Talk
Place: Room 507, Building G
Time
Chairman
Speaker/Title
15:40---16:10
16:10---16:40
16:40---17:10
Lianzhu Zhang
Xiamen University
Pfaffian Graphs Embedding on the Torus
Yijia Chen
Shanghai Jiao Tong University
Xiaodong Zhang
The Parameterized Complexity of K-edge Induced Subgraphs
Yuqin Sun
Shanghai University of Electric Power
A Bound for Size Ramsey Numbers of Multi-partite Graphs
17:30
Pujiang night tour（Including dinner） 浦江夜游(含晚餐)
Note: For those who join Pujiang night tour，please gather in front of Lehu Building at 5:30 PM. For those who do not join Pujiang night tour，you may
have dinner in the dining room of Lehu Building.
友情提示：参加浦江夜游的来宾请在下午 5：30 于乐乎楼门前集合。不参加浦江夜游的来宾可以在乐乎新楼餐厅享用我们提供的套餐。
VIII
October 31, 2011 (Monday)
Section Talk
Time
7:00---8:00
Place: Lecture Hall of Lehu Building 乐乎新楼报告厅
Breakfast: Dining Room of Lehu Building 乐乎新楼餐厅
Speaker/Title
8:30---9:00
Chairman
Moo Young Sohn
Changwon National University, Korea
Bondage Number of the Graph Bundle Having Reflection Voltage Assignment
9:00---9:30
Hye Kyung Kim
Catholic University of Deagu, Korea
Maocheng Cai
Note on Paired-domination Games
9:30---10:00
Han Ren
East China Normal University
Finding More Short Cycles in (Embedded) Graphs
10:00---10:20
Tea Break
IX
October 31, 2011 (Monday)
Section Talk
Place: Lecture Hall of Lehu Building 乐乎新楼报告厅
Time
Speaker/Title
10:20---10:50
10:50---11:20
11:20---11:50
Huiqing Liu
Hubei University
Fault-tolerant Maximal Local-connectivity on Bubblesort Star Graphs
Yanmei Hong
Shanghai University
Non-separating Cycles Avoiding Specific Vertices
Xiumei Wang
Zhengzhou University
Characterizations of PM-compact Bipartite and Near-bipartite Graphs
12:00---13:30
Chairman
Lunch: Dining Room of Lehu Building 乐乎新楼餐厅
X
Prabhu Manyem
Contents
Plenary Talks
Nick Wormald, Cops and Robber on a Random Graph ................................................................... 1
Ding-Zhu Du, Routing Cost Constrained Connected Dominating Sets ............................................ 2
Xuding Zhu, Some Problems on Circular Colouring of Graphs ...................................................... 3
Zhicheng Gao, Asymptotic Properties of Locally Restricted Compositions ..................................... 4
Beifang Chen, Tutte Type Polynomials From Viewpoint of Homology and Cohomology ................ 5
Sanming Zhou, Symmetric Graphs and Transitive Block Designs ................................................... 6
Invited Talks
Xiaodong Hu, Improving Performances of Selfish Ring Routing via Limited Cooperations ............ 7
Guochuan Zhang, Approximation Algorithms for a Bi-level Knapsack Problem ............................. 8
Yusheng Li, Remarks for the Local Lemma...................................................................................... 8
Guochun Tang, A Revised Proof of the Optimality for the Kise–Ibaraki–Mine Algorithm .............. 9
Jianliang Wu, Total Coloring of Planar Graphs Without Intersecting Short Cycles ........................ 9
Zhiyi Tan, Scheduling with Machine Maintenance for Minsum Criteria ....................................... 10
Weifan Wang, The Surviving Rate of a Planar Graph ................................................................... 10
Hong Zhu, Arithmetic Operations over Regular Languages .......................................................... 10
Liming Xiong, An Extension of the Chvάtal-Erdös Theorem: Counting the Number of Maximum
Independent Sets ............................................................................................................................. 11
Xujin Chen, Bonds with Parity Constraints .................................................................................... 19
Zhiquan Hu, A Lower Bound of Circumferences Involving Connectivities and Independence
Numbers of Subgraphs .................................................................................................................... 12
Xiaoguang Bao, Improved Approximation Algorithms for the Clustered Traveling Salesman
Problem ........................................................................................................................................... 13
Yuehua Bu, BB-coloring of Planar Graphs .................................................................................... 14
Kejun Zhao, Fully Polynomial Approximation Schemes for Two-agent Scheduling on Parallel
Machines ......................................................................................................................................... 14
Michel Habib, Algorithms for Some H -join Decompositions of Graphs...................................... 15
Yaokun Wu, A 4 -sweep LBFS Certifying Algorithm for Recognizing Interval Graphs ............... 16
Min Xu, On the Restricted Forwarding Index Problem in Communication Networks ................... 16
Jiming Guo, On the Laplacian Spectral Radius of Graphs ........................................................... 17
Changhong Lu, Identifying Codes and Locating-dominating Sets on Paths and Cycles ................ 17
Lianzhu Zhang, Pfaffian Graphs Embedding on the Torus ............................................................ 18
Yijia Chen, The Parameterized Complexity of K-edge Induced Subgraphs ................................... 19
Yuqin Sun, A Bound for Size Ramsey Numbers of Multi-partite Graphs ....................................... 19
Moo Young Sohn, Bondage Number of the Graph Bundle Having Reflection Voltage Assignment
......................... 20
Hye Kyung Kim, Note on Paired-domination Games .................................................................... 20
Han Ren, Finding More Short Cycles in (Embedded) Graphs........................................................ 21
I
Huiqing Liu, Fault-tolerant Maximal Local-connectivity on Bubblesort Star Graphs................... 21
Yanmei Hong, Non-separating Cycles Avoiding Specific Vertices................................................. 22
Xiumei Wang, Characterizations of PM-compact Bipartite and Near-bipartite Graphs ............... 23
II
Plenary Talks
Cops and Robber on a Random Graph
Nick Wormald
University of Waterloo
nwormald@uwaterloo.ca
Coauthor: Pawel Pralat
Abstract: In the game of cops and robber, the cops try to capture a robber moving on
the vertices of the graph. The minimum number of cops required to win on a given
graph G is called the cop number of G. The biggest open conjecture in this area is
Meyniel's, which asserts that for some absolute constant C , the cop number of every
graph G is at most C n where n | V (G) |. We show that Meyniel's conjecture holds
asymptotically almost surely for G a random d -regular graph, d  3 as well as in the
standard random graph model G (n, p). Joint work with Pawel Pralat.
1
Routing Cost Constrained Connected
Dominating Sets
Ding-Zhu Du
University of Texas at Dallas
dzdu@utdallas.edu
Abstract: In wireless networks, the connected dominating set (virtual backbone)
plays an important role in topological control. Using the connected dominating set
can reduce routing table size and communication cost. However, the length of
routing path may increase, which may cause time delay; also, the road load
balancing may get worse. To improve the performance of the connected dominating
set, One has studied the routing cost constrained connected dominating set. In this
talk, we present some new developments along this research direction.
2
Some Problems on Circular Colouring of
Graphs
Xuding Zhu
Zhejiang Normal University
xudingzhu@gmail.com
Abstract: Given a real number r and a graph G , a circular r -colouring of G colours
vertices of G with points in a circle of circumference r so that colours assigned to
adjacent vertices are at least distance 1 apart. The circular chromatic number  c (G)
of G is the infimum of those r for which G has a circular r -colouring. The circular
chromatic number of a graph is a refinement of its chromatic number. It contains more
information about the structure of the graph. The concept of circular colouring of
graphs has attracted considerable attention in the past twenty years, and has become
an important branch of chromatic graph theory. There are many exciting results and
new techniques, as well as many challenging open problems. This talk presents some
open problems in this area.
3
Asymptotic Properties of Locally Restricted
Compositions
Zhicheng Gao
University of Macao & Carleton University
zgao@math.carleton.ca
Abstract: Roughly speaking, a locally restricted composition is a composition of an
integer in which parts within a given distance of each other are required to satisfy
some conditions. Carlitz compositions, in which adjacent parts must be distinct, are a
classic example of such compositions. Compositions with local restrictions are
usually much more complicated than unrestricted compositions from enumerative
viewpoint. We survey some recent results about the asymptotic behavior of locally
restricted compositions including number, joint normality of many parameters,
largest part, and probability of gap-free. We use combinatorial arguments, generating
functions and infinite transfer matrices.
4
Tutte Type Polynomials from Viewpoint of
Homology and Cohomology
Beifang Chen
HongKong University of Science and Technology
mabfchen@ust.hk
Abstract: The Tutte polynomial is a common generalization of the chromatic
polynomial and the flow polynomial. It is well-known that the value of the flow
polynomial at a positive integer q is the number of nowhere-zero flows over an
abelian group of q elements. This can be considered as counting the number of
homology cycles which are nowhere-zero in the homology group. The chromatic
polynomial is analogous when it is reduced to the tension polynomial which comes
from the counting of nowhere-zero tensions in the cohomology group. I shall
combine counting inside the homology and cohomology together to redefine the
Tutte polynomial which automatically gives rise to a combinatorial/geometric
interpretations for the Tutte polynomial and its likes. The homology group in the talk
is termed as flow group while the cohomology group is termed as tension group.
5
Symmetric Graphs and Transitive Block
Designs
Sanming Zhou
University of Melbourne
sanming@unimelb.edu.au
Abstract: Exploring symmetry of geometric objects has always been a fascinating
topic in mathematics. In particular, in graph theory, since Tutte's seminal work (1947)
on cubic symmetric graphs, there have been extensive researches on symmetries of
graphs, which are usually measured in terms of their automorphism groups. In the
case when the automorphism group of a graph contains a subgroup which is
transitive on the set of arcs, the graph is said to be symmetric, where an arc is an
ordered pair of adjacent vertices. Often the subgroup involved is imprimitive on the
vertex set of the graph, that is, it leaves at least one nontrivial partition invariant. In
this talk I will discuss recent progress on the study of imprimitive symmetric graphs
with an emphasis on their connections with transitive block designs.
Keywords: Symmetric graph, arc-transitive graph, block design.
6
Invited Talks
Improving Performances of Selfish Ring
Routing via Limited Cooperations
Xiaodong Hu
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
xdhu@amss.ac.cn
Abstract: Selfish routing models network routing from a game-theoretic perspective, in
which network users are viewed as self-interested strategic players participating in a
competitive game. Each player, with his own pair of source and destination in the network,
aims to establish a communication path (between his source and destination) along which he
would experience latency or load as low as possible, given the link congestion caused by all
other players. Despite the system objective to minimize the maximum latency among all
source-destination pairs, network designers are often interested in a Nash equilibrium (NE)
that is as close to the system optimum as possible, where the NE is a “stable state” among the
players, from which no player has the incentive to deviate unilaterally. The (in)efficiency of
NE is predominantly quantified by the so called price of anarchy (PoA), which is the
worst-case ratio between the maximum latencies/load in a NE and in a system optimum. In
this talk we will show that PoAs could be reduced via cooperation among only a small
number of players, where k players cooperate only if none of them would experience a
higher latency/load and at least one would experience a lower latency/load when simultaneous
changing their routes.
7
Approximation Algorithms for a Bi-level
Knapsack Problem
Guochuan Zhang
Zhejiang University
zgc@zju.edu.cn
Abstract: We consider a variant of the knapsack problem. There are two knapsacks
with probably different capacities, owned by two agents, respectively. Given a set of
items, each with a fixed size and a profit, the two agents select items and pack them
into their own knapsacks under the capacity constraint. Same items can be packed
simultaneously into different knapsacks. However, in this case the profit of such
items may vary. One agent aims to maximize the total profit of items packed into her
knapsack, while another agent can only pack items into her knapsack as well but she
cares about the total profit of both knapsacks. The latter agent is a leader while the
former is a follower. We are interested in designing approximation algorithms for the
leader assuming that the follower is selfish. For different settings we provide
approximation results.
Remarks for the Local Lemma
Yusheng Li
Department of Mathematics, Tongji University
Li_yusheng@tongji.edu.cn
Abstract: Following an idea of Erdos and Spencer, it is shown that the dependency
graph in the local lemma can be replaced by a sparser graph, which is a bipartite
graph for most applications. This form can be used to improve the known results or
simplify the previous proofs.
8
A Revised Proof of the Optimality for the
Kise–Ibaraki–Mine Algorithm
Guochun Tang
Shanghai Second Polytechnic University
gctang@sspu.cn
Abstract: For the problem of scheduling n -jobs on one-machine with agreeable job
release dates and due dates to minimize the number of late jobs, Kise, Ibaraki and
Mine [Operations Research, 26 (1978) 121–126] gave an O(n 2 ) -time algorithm and
proved its optimality by four lemmas. Li et al. [Operations Research, 58 (2010)
508–509] gave a counterexample to show that one lemma is invalid in some case and
therefore the optimality is also invalid. In this paper, we revise the lemma and prove
that the algorithm is still valid.
Total Coloring of Planar Graphs without
Intersecting Short Cycles
Jianliang Wu
Shandong University
jlwu@sdu.edu.cn
Abstract: Let G be a planar graph with (G )  8 and for each vertex x, there is an
integer k x {3, 4,5, 6, 7,8} such that G has at most one k x -cycle incident with x.
Then the total chromatic number of G is   1.
9
Scheduling with Machine Maintenance for
Minsum Criteria
Zhiyi Tan
Zhejiang University
tanzy@zju.edu.cn
Abstract: In the talk, we study scheduling problems with machine maintenance on
single or parallel machines. There are machine nonavailability periods/operator
nonavailability periods on some of the machines. If a job cannot be finished before a
nonavailability period, it has to restart rather than continue. No job can be started or
finished during the operator nonavailability period. The objective is to minimize the
total completion time. Worst-case ratios of SPT and nonapproximability results are
obtained for different situations.
The Surviving Rate of a Planar Graph
Weifan Wang
Zhejiang Normal University
wwf@zjnu.cn
Abstract: In this talk, we give a brief survey on the surviving rate of a graph. In
particular, we discuss the surviving rate of planar graphs with high girth.
Arithmetic Operations over Regular
Languages
Hong Zhu
East China Normal University
hzhu@sei.ecnu.edu.cn
Abstract: Regular language is a classic topic in theory of computation. We consider
10
the closure of arithemetic operations over the binary numbers if the numbers come
from strings in the regular sets.
An Extension of the Chvάtal-Erdös Theorem:
Counting the Number of Maximum
Independent Sets
Liming Xiong
Department of Mathematics, Beijing Institute of Technology
lmxiong@bit.edu.cn
Abstract: In 1972, Chvάtal and Erdös proved a well-known result that the graph G
with connectivity  (G ) not less than its independence number  (G ) is hamiltonian.
We will strengthen the Chvάtal-Erdös theorem to the following: Let G be a simple
2 -connected graph of order n  2 2 (G) such that  (G )   (G )  1 and such that the
number of maximum independent sets of cardinality  (G )  1 is at most n  2 (G ).
Then G is either Hamiltonian or a subgraph of Kk  ((kK1 )  Kn2k ). In this talk, we
also present some other extensions of the Chvάtal-Erdös theorem.
Bonds with Parity Constraints
Xujin Chen
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
xchen@amss.ac.cn
Coauthors: Guoli Ding, Xingxing Yu, Wenan Zang
Abstract: Given a connected graph G  (V , E ) and three even-sized subsets A1 , A2 ,
A3  of V , when does V  have a partition (S1, S2 ) such that G[ Si ] is connected
11
and  Si  Aj  is odd for all i  1,2 and  j  1,2, This problem arises in the area of
integer flow theory and has theoretical interest in its own right. The special case when
A1  A2  A3  2 has been resolved by Chakravarti and Robertson, and the general
problem can be rephrased as a problem on binary matroids that asks if a given triple
of elements is contained in a circuit. We present a complete solution to this problem
based on a strengthening of Seymour's theorem on triples in matroid circuits (Joint
work with Guoli Ding, Xingxing Yu, and Wenan Zang).
A Lower Bound of Circumferences Involving
Connectivities and Independence Numbers of
Subgraphs
Zhiquan Hu
Faculty of Mathematics and Statistics, Central China Normal University
Hu_zhiq@yahoo.com.cn
Coauthors: Guantao Chen, Yaping Wu
Abstract: Let G be a k -connected graph of order n and let  and c (G ) be the
independence number of G and the circumference of G , respectively. If   k ,
Chvάtal and Erdӧs showed that G is hamiltonian. For   k  2, Fouquet and
Jolivet in 1978 made the conjecture that c(G ) 
k (n    k )
, which was recently

confirmed by Suil O, D. B. West and H. Wu. Under the same condition, we obtained
the following two results:
1. c(G )  min{ n, max{
k (n    k )

 n  2  2k 
,k
}};



2. For every nonempty induced subgraph H , there is a cycle C in G such that
 H   (H )  k 
V (C )  V ( H )  min{ H , k 
}.
 (H )


12
Set f (G ) : min{ G , max{
k G   (G )  k
 (G )
 G  2 (G )  2k 
,k
}}. Notice that f (G )
 (G )


is not monotonic according to the inclusion order of subgraphs. We further improve
the first result by showing that
c(G )  max{ f ( H ) : H is any nonempty induced subgraph of G}.
The second result is related to the concept of cyclability of subgraphs.
Improved Approximation Algorithms for the
Clustered Traveling Salesman Problem
Xiaoguang Bao
East China University of Science and Technology
xgbao0106@163.com
Abstract: Given a weighted undirected graph G  (V , E ), where the vertex set V  is
partitioned into K  clusters V1 , VK  the clustered traveling salesman problem is to
compute a shortest tour so that all vertices are visited and the vertices of each cluster
are visited consecutively. For the case in which the starting vertex of each cluster is
given while the ending vertex is free to be selected, we present a 5 2 -approximation
algorithm, and for the case in which no starting and ending vertices of any cluster are
specified, we present a 19 10 -approximation algorithm. Both algorithms make
improvements on the respective ones of Guttmann-Beck, Hassin, Khuller, and
Raghavachari [Algorithmica, 28 (2000) 422-437].
Keywords: Traveling salesman problem, clustered traveling salesman problem,
approximation algorithm.
13
BB-coloring of Planar Graphs
Yuehua Bu
College of Mathematics Physics and Information Technology, Zhejiang Normal University
yhbu@zjnu.edu.cn
Abstract: Let H  be a spanning subgraph of G , a BB-coloring of (G, H ) is a
mapping  f : V (G)  1, 2,
, k , such that (1)  f (u)  f (v)  2, if uv  E ( H ); (2)
f (u)  f (v)  1 of uv  E (G )  E ( H ). The minimal number k such that (G, H )
has a BB-k-coloring, is called the BB-chromatic number of (G, H ), and is denoted
by b (G, H ).
For BB-coloring of planar graphs, we mainly discuss two problems as follows:
Problem 1: Let T  be any spanning tree of a connected planar graph G , prove that
b (G, T )  7 without using Four Color Theorem.
Problem 2: What’s the precise value of the minimal number   such that for each
planar graph with g (G )   , there exists a spanning tree T  and
b (G, T )  4.
Keywords: BB-coloring, panning tree, cycle, planar graph.
Fully Polynomial Approximation Schemes for
Two-agent Scheduling on Parallel Machines
Kejun Zhao
Department of Mathematics, School of Science, East China University of Science and
Technology
Zhaokejun0711@163.com
Coauthor: Xiwen Lu
14
Abstract: Two models of two-agent scheduling on m identical machines are
considered in this paper. In both models, we aims at minimizing the makespan and
the sum of completion time of agent A respectively, while keeping the makespan of
agent B no more than a factor Q  0. We proved that these two problems are
NP-hard and can be solved in pseudo-polynomial time. And two FPTASs are
designed respectively.
Algorithms for Some H -join Decompositions
of Graphs
Michel Habib
University Paris Diderot - Paris7
habib@liafa.jussieu.fr
Abstract: A homogeneous pair (also known as  -module) of a graph is a pair
{M1 , M 2 } of disjoint vertex subsets such that for every vertex x  ( M1
M 2 ) and
i  {1, 2}, x is either adjacent to all vertices in M i  or to none of them. First used in the
context of perfect graphs [Chvátal and Sbihi 1987], it is a generalization of splits
(a.k.a  -joins) and of modules. The algorithmics to compute them appears quite
involved. In this talk I will describe an O(mn 2 ) -time algorithm computing (if any) a
homogeneous pair, which not only improves a previous bound of O(mn3 ) [Everett,
Klein and Reed 1997], but also uses a nice structural property of homogenous pairs.
Our result can be extended to compute the whole homogeneous pair decomposition
tree, within the same complexity. Using similar ideas, we present an O(nm2 ) -time
algorithm to compute a N -join decomposition of a graph, improving a previous
O(n6 ) algorithm. These two decompositions are special case of H -joins [Bui-Xuan,
15
Telle and Vatshelle 2010] to which these techniques apply.
A 4 -sweep LBFS Certifying Algorithm for
Recognizing Interval Graphs
Yaokun Wu
Department of Mathematics, Shanghai Jiao Tong University
ykwu@sjtu.edu.cn
Abstract: In the literature, the only known linear time certifying algorithm for
recognizing interval graphs is reported by Kratsch et al. [1] in 2006. This algorithm
relies on the so-called MPQ tree data structure. Based on the LBFS structure theory
developed by Corneil et al. [2], Peng Li and I recently develop a new linear time
certifying algorithm for recognizing interval graphs which does not require any
complicated data structure and basically only consists of 4-sweeps of Lexicographic
Breadth-First Search. This talk is about this new algorithm and relevant topics.
On the Restricted Forwarding Index Problem
in Communication Networks
Min Xu
Beijing Normal University
xum@bnu.edu.cn
Abstract: In a communication network, it is desired that all pairs of nodes can
exchange messages at the same time. But under the capacity constraints on nodes or
links, this desired property may not be satisfied, only some of node pairs can
communicate each other while the rest of others have to be blocked. A natural
question is at most how many node pairs can communicate synchronously with the
load restriction? In this paper, we first show that the problem is NP-complete. Then
16
we present two approximation algorithms for the problems under the node load
constraint and the link load constraint, respectively.
On the Laplacian Spectral Radius of Graphs
Jiming Guo
Department of mathematics, China University of Petroleum
jimingguo@hotmail.com
Abstract: The Laplacian spectral radius of a graph is the largest eigenvalue of its
Laplacian matrix. In this report, we investigate how the Laplacian spectral radius
changes under some perturbations.
Identifying Codes and Locating-dominating
Sets on Paths and Cycles
Changhong Lu
East China Normal University
chlu@math.ecnu.edu.cn
Coauthors: Chunxia Chen, Zhengke Miao
Abstract: Let G  (V , E ) be a graph and let r  1 be an integer. For a set D  V ,
define Nr [ x]  { y V : d ( x, y)  r} and Dr ( x)  Nr [ x] D, where d ( x, y ) denotes the
number of edges in any shortest path between x and y. D is known as an
r -identifying code ( r -locating-dominating set, respectively), if for all vertices
x  V ( x V \ D, respectively), Dr ( x) are all nonempty and different. Roberts and
Roberts [Locating sensors in paths and cycles: The case of 2 -identifying codes,
European Journal of Combinatorics, 29 (2008) 72-82] provided complete results for
the paths and cycles when r  2. In this paper, we provide complete results in cycles
17
and paths for r -identifying codes; we also give complete results for
2 -locating-dominating sets in cycles, which completes the results of Bertrand et al.
[Identifying and locating-dominating codes on chains and cycles, European Journal
of Combinatorics 25, (2004) 969-987]. This work is jointed with Chunxia Chen and
Zhengke Miao.
Pfaffian Graphs Embedding on the Torus
Lianzhu Zhang
Xiamen University
zhanglz@xmu.edu.cn
Abstract: An orientation of a graph G with even vertices is Pfaffian if every even
cycle C such that G \ V (C ) has a perfect matching has an odd number of edges
directed in either direction of the cycle. The significance of Pfaffian orientations
stems from the fact that if a graph G has one, then the number of perfect matchings
of G can be computed in polynomial time. So it makes sense to study the question:
“Whether a graph has a Pfaffian orientation?” There is a classical result of Kasteleyn
(1967) that every planar graph has a Pfaffian orientation. In 1975, Little proved an
elegant characterization of bipartite graphs that admit a Pfaffian orientation. In 2001,
Fischer and Little characterized Pfaffian near bipartite graphs. In this paper, we
prove a sufficient condition for Pfaffian graphs embedding on the torus. Furthermore,
we show that all quadratic lattices on the torus are Pfaffian iff they are not bipartite
graphs.
18
The Parameterized Complexity of k-edge
Induced Subgraphs
Yijia Chen
Shanghai Jiao Tong University
yijia.chen@cs.sjtu.edu.cn
Abstract:
We
prove
that
finding
a
k-edge
induced
subgraph
is
fixed-parameter tractable, thereby answering an open problem of Leizhen Cai. Our
algorithm is based on several combinatorial observations, Gauss' famous E ureka
theorem, and a generalization of the well-known fpt-algorithm for the
model-checking problem for first-order logic on graphs with locally bounded
tree-width due to Frick and Grohe. On the other hand, we show that two natural
counting versions of the problem are hard. Hence, the k-edge induced subgraph
problem is one of the rare known examples in parameterized complexity that are
easy for decision while hard for counting.
A Bound for Size Ramsey Numbers of
Multi-partite Graphs
Yuqin Sun
Shanghai University of Electric Power
xxteachersyq@163.com
Abstract: It is shown that the (diagonal) size Ramsey numbers of complete
m -partite graphs Kn n  can be bounded from below by cn2 2( m1) n  where c is a
positive constant.
19
Bondage Number of the Graph Bundle Having
Reflection Voltage Assignment
Moo Young Sohn
Changwon National University, Korea
mysohn@changwon.ac.kr
Abstract: The bondage number b(G ) of a graph G is the cardinality of a smallest set
of edges whose removal from G results in a graph with a domination number greater
than the domination number of G. In this talk, we calculate that the bondage number
of the graph bundle Cn  C5  having reflection voltage assignment.
Note on Paired-domination Games
Hye Kyung Kim
Catholic University of Deagu, Korea
hkkim@cu.ac.kr
Abstract: Various variants of dominating set games were introduced and it was
shown that for each variant, a rigid game being balanced is equivalent to a relaxed
game being balanced. It is natural to ask if for any other variant of dominating set
game, the balancedness of a rigid game and the balancedness of a relaxed game are
equivalent. In this paper, we show that the answer for the question is negative by
considering the rigid and relaxed paired-domination games, which is considered as a
variant of dominating set games. We characterize the cores of both games and show
that the rigid game being balanced is not equivalent to the relaxed game being
balanced. In addition, we study the cores of paired-dominations games on paths and
cycles.
20
Finding More Short Cycles in
(Embedded) Graphs
Han Ren
Department of Mathematics, East China Normal University
hren@math.ecnu.edu.cn
Abstract: In this talk we introduce a generalized fundamental cycle method which is
useful in locating short cycles not satisfying the famous 3-path-condition of
C.Thomassen. Our result will show that there are polynomiaolly many shortest
cycles, shortest even cycles, shortest contractible cycles etc in a given graph.
Fault-tolerant Maximal Local-connectivity
on Bubblesort Star Graphs
Huiqing Liu
Hubei University
hql_2008@163.com
Abstract: An interconnection network is usually modeled as a graph, in which ertices
and edges correspond to processor and communication links, respectively.
Connectivity is an important measurement for the fault tolerant in interconnection
network. Two vertices is maximally local-connected if the maximum number of
internally vertex-disjoint paths between them equals the minimum degree of these two
vertices. In this paper, we show that an n -dimensional Bubblesort star graph is
(2n  5) -fault-tolerant maximally local-connected and it is also (2n  6) -fault-tolerant
one-to-many maximally local-connected.
21
Non-separating Cycles Avoiding Specific
Vertices
Yanmei Hong
Department of Mathematics, Shanghai University
lovely-hym@163.com
Coauthors: Liying Kang, Xingxing Yu
Abstract: Thomassen proved that every (k  3) -connected graph G contains an
induced cycle C such that G  V (C ) is k -connected, establishing a conjecture of
Lovász. It becomes very difficult if one requires C go through a specified edge and
avoid a given set of vertices. For any positive integers k ,l , does there exist a smallest
positive integer g (k , l ) such that for any g (k , l ) -connected graph G , any  X  V (G )
with | X | k , and any e  E (G  X ), there is an induced cycle C in G  X  such that
e  E (C ) and G  V (C ) is l -connected? The case when  X   is a well-known
conjecture of Lovász which is still open for k  3. In this paper, we prove
g (k ,1)  10k  1 and  g (k , 2)  10k  11. We also consider a weaker version: For any
positive integers k ,l , is there a smallest positive integer  f ( k , l ) such that for every
f ( k , l ) -connected graph G and any  X  V (G ) with  X | k , there is an induced
cycle C in G  X  such that G  V (C ) is l -connected? The case when  X   was
studied by Thomassen. We prove  f (k , l )  2k  l  2 and  f (k ,1)  k  3.
22
Characterizations of PM-compact Bipartite
and Near-bipartite Graphs
Xiumei Wang
Zhengzhou University
wangxiumei@zzu.edu.cn
Abstract: The perfect matching polytope of a graph is the convex hull of the
incidence vectors of all perfect matchings in this graph. A graph is called perfect
matching compact (shortly, PM-compact), if its perfect matching polytope has
diameter one. This paper characterizes PM-compact bipartite and near-bipartite
graphs.
23
Email Address List
No.
Name
Institute
Email
1
Xiaoguang Bao
East China University of Science
and Technology
xgbao0106@163.com
2
Yanqin Bai
Shanghai University
yqbai@staff.shu.edu.cn
3
Baoyin-Dureng
Xinjiang University
baoyin@xju.edu.cn
4
Chunsong Bo
Shanghai University
bcs2018@163.com
5
Yuehua Bu
Zhejiang Normal University
yhbu@zjnu.edu.cn
6
Maocheng Cai
Academy of Mathematics and
Systems
Science,
Chinese
Academy of Sciences
caimc@iss.ac.cn
7
Xinguo Cao
Shanghai University
caoxinguo2008@163.com
8
An Chang
Fuzhou University
anchang@fzu.edu.cn
9
Beifang Chen
HongKong University of Science
and Technology
mabfchen@ust.hk
10
Xujin Chen
Academy of Mathematics and
Systems
Science,
Chinese
Academy of Sciences
xchen@amss.ac.cn
11
Yan Chen
Shanghai University
chenyan_shu@hotmail.com
12
Yaojun Chen
Nanjing University
yaojunc@nju.edu.cn
13
YiJia Chen
Shanghai Jiao Tong University
yijia.chen@cs.sjtu.edu.cn
14
Yukun Chen
Zhejiang University of Finance
& Economics
ykcheng@amss.ac.cn
15
Ding-Zhu Du
University of Texas at Dallas,
USA
dzdu@utdallas.edu
16
Qizhi Fang
Ocean University of China
qfang@ouc.edu.cn
17
Lihua Feng
Shandong Institute of Business
and Technology
fenglh@163.com
18
Zhicheng Gao
University of Macao & Carleton
University
zgao@math.carleton.ca
19
Jiming Guo
China University of Petroleum
jimingguo@hotmail.com
20
Michel Habib
University Paris
Paris7, France
21
Miaomiao Han
Shanghai University
abcdhanmiao@126.com
22
Yanmei Hong
Shanghai University
lovely-hym@163.com
23
Xinmin Hou
University of Science
Technology of China
24
Xiaodong Hu
Academy of Mathematics and
Systems
Science,
Chinese
Academy of Sciences
Diderot
-
and
habib@liafa.jussieu.fr
xmhou@ustc.edu.cn
xdhu@amss.ac.cn
25
Zhiquan Hu
Central
University
China
Normal
Hu_zhiq@yahoo.com.cn
26
Zhiming Huo
Shanghai University
mingchuen456@163.com
27
Hengwu Jiang
Shanghai University
5westlife@163.com
28
Liying Kang
Shanghai University
lykang@shu.edu.cn
29
Hye Kyung Kim
Catholic University of Deagu,
Korea
hkkim@cu.ac.kr
30
Lu Kong
Shanghai University
kllzy@163.com
31
Jianping Li
Yunnan University
jianping@ynu.edu.cn
32
Shan Li
Shanghai University
shanonleesnow@126.com
33
Wenhua Li
Zhengzhou University
liwenhua@zzu.edu.cn
34
Xiangwen Li
Huazhong Normal University
xwli2808@yahoo.com
35
Yusheng Li
Tongji University
Li_yusheng@tongji.edu.cn
36
Zuosong Liang
Shanghai University
shuxueyunchou@163.com
37
Huiqing Liu
Hubei University
hql_2008@163.com
38
Xiaolei Liu
Shanghai University
liuxiaoleiangel@yahoo.com.cn
39
Zhaohui Liu
East China University of Science
and Technology
zhliu@ecust.edu.cn
40
Changhong Lu
East China Normal University
chlu@math.ecnu.edu.cn
41
Xiwen Lu
East China University of Science
and Technology
xwlu@ecust.edu.cn
42
Prabhu Manyem
Shanghai University
manyem@gmail.com
43
Zhengke Miao
Xuzhou Normal University
zkmiao@xznu.edu.cn
44
Han Ren
East China Normal University
hren@math.ecnu.edu.cn
45
Erfang Shan
Shanghai University
efshan@shu.edu.cn
46
Jiayu Shao
Tongji University
jyshao@sh163.net
47
Jinlong Shu
East China Normal University
jwshu@math.ecnu.edu.cn
48
Moo Young Sohn
Changwon National University,
Korea
mysohn@changwon.ac.kr
49
Qiang Sun
Shanghai University
qsun1987@163.com
50
Yuqin Sun
Shanghai University of Electric
Power
xxteachersyq@163.com
51
Zhiyi Tan
Zhejiang University
tanzy@zju.edu.cn
52
Guochun Tang
Shanghai Second Polytechnic
University
gctang@sspu.cn
53
Dingguo Wang
Chongqing Normal University
wangdg2955@sina.com
54
Hechao Wang
Shanghai University
dreamingsuper@shu.edu.cn
55
Haichao Wang
Shanghai University of Electric
Power
whchao2000@163.com
56
Hongzhuan Wang
Shanghai University
hongzhuanwang@gmail.com
57
Qingwen Wang
Shanghai University
wqw@staff.shu.edu.cn
58
Weifan Wang
Zhejiang Normal University
wwf@zjnu.cn
59
Wenhuan Wang
Shanghai University
whwang@shu.edu.cn
60
Xiaoxia Wang
Shanghai University
xiaoxiawang@shu.edu.cn
61
Xiumei Wang
Zhengzhou University
wangxiumei@zzu.edu.cn
62
Qi Wei
Shanghai University
weiqi@nit.zju.edu.cn
63
Nick Wormald
University of Waterloo, Canada
nwormald@uwaterloo.ca
64
Jianliang Wu
Shandong University
jlwu@sdu.edu.cn
65
Yaokun Wu
Shanghai Jiao Tong University
ykwu@sjtu.edu.cn
66
Mao Xiao
Shanghai University
870201550@qq.com
67
Liming Xiong
Beijing Institute of Technology
lmxiong@bit.edu.cn
68
Min Xu
Beijing Normal University
xum@bnu.edu.cn
69
Weiwei Xu
Shanghai University
xuweiweishuxue@126.com
70
Yongjian Yang
Shanghai University
yjyang@shu.edu.cn
71
Tingting Ye
Shanghai University
06120046@163.com
72
Xiying Yuan
Shanghai University
xiyingyuan@shu.edu.cn
73
Guihai Yu
Shandong Institute of Business
and Technology
yuguihai@126.com
74
Guochuan Zhang
Zhejiang University
zgc@zju.edu.cn
75
Hongjuan Zhang
Shanghai University
zhanghongjuan@shu.edu.cn
76
Li Zhang
Tongji University
lizhang@tongji.edu.cn
77
Li Zhang
Shanghai Finance University
zhanglizp@163.com
78
Lianzhu Zhang
Xiamen University
79
Xiaodong Zhang
Shanghai Jiao Tong University
zhanglz@xmu.edu.cn
xiaodong@sjtu.edu.cn
80
Chengye Zhao
China Jiliang University
zhao_cy@163.com
81
Kejun Zhao
East China University of Science
and Technology
zhaokejun0711@163.com
82
Min Zhao
China Jiliang University
minzhao@126.com
83
Sanming Zhou
University
Australia
sanming@unimelb.edu.au
84
Weiya Zhong
Shanghai University
wyzhong@shu.edu.cn
85
Hong Zhu
East China Normal University
hzhu@sei.ecnu.edu.cn
86
Xuding Zhu
Zhejiang Normal University
xudingzhu@gmail.com
of
Melbourne,