COURSE SYLLABUS
Course Prefix/Number: MAD5305
Course Title: Graphs and their Applications
Course Credit Hours: 3
Instructor Name and Contact Information:
Dr. Jaromy Kuhl
Room 439, Bldg. 04, Ext. 7702
E-mail: jkuhl@uwf.edu
Prerequisites or Co-Requisites: Pre/Co requisites: Set Theory and Mathematical Logic (MHF 3202)
Course Description:
The MAD5303 course is devoted to graphs and the various ways they are used to model problems. In
this course you will study some structures found in graphs such as hamiltonian cycles, matchings, and
subdivisions and you will study some graph invariants such as connectivity, the chromatic number, and
the chromatic index.
Student Learning Outcomes:
At the completion of the course students will be able to
 explain the basic concepts of a graph.
 explain the concept of a matching in a graph and prove Hall’s theorem.
 demonstrate algorithms related to stable matchings.
 explain the concepts of connectivity and k-connectivity and prove Menger’s theorem.
 properly color the vertices and edges of a graph and prove Vizing’s theorem and Brook’s
theorem.
 apply edge coloring results to problems involving latin squares
 determine small ramsey numbers
 define a planar graph and prove Kuratowski’s theorem.
 use graphs to model certain real life problems and show how graph theoretic methods can be
used to solve these problems.
Topics Covered:
1. Introduction to graphs
 Directed and undirected graphs and basic terminology
 Graphs as models
 Common graphs (complete graphs, bipartite graphs, trees, etc.)
 Vertex degrees
 Paths and cycles
 Isomorphisms
2. Party problems
 Assignment problems
 Maximum matchings
 Hall’s theorem
 The Gale-Shapely algorithm for stable matchings
 Friendship/stranger problems
 Ramsey numbers
3. Connection problems
 Vertex- and edge-connectivity
 Blocks of a graph
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
k-connected graphs
Menger’s theorem
4. Scheduling problems
 Vertex colorings
 Vizing’s theorem
 Edge colorings
 Brook’s theorem
 Latin Squares (Ryser’s theorem)
5. Transportation problems
 Konigsberg bridge problem
 Euler circuits and walks
 Traveling salesman problem
 Hamiltonian cycles in graphs
 Longest cycles in graphs
6.
Planar Graphs
 The 3 houses and 3 utilities problem
 Euler’s formula
 Kuratowki’s Theorem
 The five color theorem for planar graphs
 Graph surfaces (Dr. Marx)
7. Directed Graphs
 Competition graphs
 Competition numbers
Tentative Schedule:
Week 1: (8/22 – 8/26)
Introduction to graphs
Week 2: (8/29 – 9/2)
Introduction to graphs
Week 3: (9/5 – 9/9)
Party problems
Week 4: (9/12 – 9/16)
Party problems
Week 5: (9/19 – 9/23)
Connection problems
Week 6: (9/26 – 9/30)
Test 1, Scheduling problems
Week 7: (10/3 – 10/7)
Scheduling problems
Week 8: (10/10 – 10/14)
Scheduling problems
Week 9: (10/17 – 10/21)
Transportation problems
Week 10: (10/24 – 10/28)
Transportation problems
Week 11: (10/31 – 11/4)
Test 2, Planar graphs
Week 12: (11/7 – 11/11)
Graph Surfaces
Week 13: (11/14 – 11/18)
Directed graphs
Week 14: (11/21 – 11/25)
Thanksgiving Holidays
Week 15: (11/28 – 12/2)
Catch-up if needed
Week 16: (12/5 – 12/9)
Test 3 (final exam week)
Classes are suspended for Labor Day (9/5/2011), Veteran’s Day (11/11/2011), and Thanksgiving
(11/24/2011 – 11/25/2011).
Required text:
Introduction to Graph Theory, 2nd edition; Douglas B. West
Grading / Evaluation:
There will be
 3 in-class tests (inclusive of final exam) each worth 100 points,
 4 projects, and
 8-10 homework assignments.
Grade calculation:
Each test is worth 20% of your final grade; the four projects are each 5% for a total of 20%; and the
average of your homework assignments makes up the remaining 20%.
Grades:
Let S be your grade.
1. A if S is in [92, 100], A- if in [90, 92)
2. B+ if in [87, 90), B if in [83, 87), B- if in [80, 83)
3. C+ if in [77,80), C if in [73, 77), C- if in [70, 73)
4. D if in [60, 70)
5. F if below 60
Final Exam:
December 8, 2011; 2:30 – 5:00 p.m.
Extra Credit:
There is none.
Examinations:
You will be given 3 exams (exam dates are 9/27, 11/01, and 12/8). You should not miss an exam unless
you have a doctor’s note explaining your sickness, a death in the family, or a university function you
cannot miss. Only under these circumstances will you be allowed a make-up test. The first and second
exams will be proctored. The third exam will be a take-home exam.
Homework:
Each week, except for test week, homework problems will be assigned. Students will be given one week
to complete the assignment.
Projects:
There will be 4 projects. Projects are to be completed individually. The purpose of these projects is to
prove an important mathematical theorem and to do so by completing a series of tasks and then piecing
the tasks together, as one would with a puzzle, for a proof of the theorem. The theorems that these
projects will investigate are Hall’s theorem, Menger’s theorem, Vizing’s theorem, and Kuratowski’s
theorem.
Office Hours: 1:00 – 4:00 pm TTh
Expectations:
I strongly recommend that you DO NOT miss class. If you do, you will miss the explanations of the text
as well as worked problems, which are crucial for doing well on tests and thus doing well in the course.
However, if you need to miss class I understand. Lecture notes, projects, and homework assignments
will be posted in eLearning. If you miss a deadline due to absence, please arrange a time with me to
submit missed projects and/or homework assignments. If you need assistance outside of the classroom,
please come to my office hours. Frequent absences will not be tolerated and will more than likely result
in an undesirable grade.
Other expectations are:
1. Please arrive to class on time.
2. Please do not walk in and out of class while class is in session.
3. Please do not talk while I am talking.
4. Please look like you’re paying attention, i.e. no newspapers, sleeping, or other textbooks.
5. Please always use a pencil.
6. Cell phones should be on silence.
7. Absolutely no texting.
About the online section:
For students enrolled from remote locations this course has an “on-line” section that uses ELLUMINATE
as the platform for instruction. The medium provides real-time instruction/communication, full two-way
audio and a live display of writing on the “white board”. Students who enroll for the on-line section should
contact the Mathematics & Statistics department (474-2276) for a demonstration of ELLUMINATE so that
they will be properly set up BRFORE classes commence.
1. Even though the section is described as “on-line” students enrolled in this section must attend
the class by logging on from the remote location at the same time class is in session. This will
allow students to actively participate in the class proceedings (i.e. ask and answer questions,
give feedback etc.)
2. The first and second exams are proctored. Students in the on-site section (face-to-face section)
will take tests in the classroom. “On-line” students must arrange (with instructor’s approval)
a suitable site to take the test at the same time in a proctored setting. There is a form that
must be filled and submitted for approval of the testing site. This form can be found at
http://uwf.edu/atc/Guide/Developing/DesignStandards/assessment/Proctor.cfm.
3. On-line students will submit project and homework assignments via the drop box in eLearning.
Students in the on-site section will submit projects and homework assignment in class.
Special Technology Utilized by Students:
All notes, supplementary notes, problem sets, assignments, projects, and articles will be uploaded to
eLearning. The discussion board in eLearning will be used frequently. Calculators are permitted but
completely unnecessary.
Withdrawal deadlines:
1. Withdrawal deadline for all courses for the term with partial refund and grade of WR is
September 16th.
2. Withdrawal deadline for individual or all courses for the term with an automatic W is October
28th.
3. Withdrawal deadline for all courses for the term with grade of W or WF at the instructor’s
discretion is December 2nd.
Students who are requesting a late withdraw from class (after March 20h), must have the approval of the
advisor, instructor, and department chairperson (in that order) and finally, by the Academic Appeals
committee. Requests for late withdraws may be approved only for the following reasons (which must be
documented):
1. A death in the immediate family.
2. Serious illness of the student or an immediate family member.
3. A situation deemed similar to categories 1 and 2 by all in the approval process.
4. Withdrawal due to Military Service (Florida Statute 1004.07)
5. National Guard Troops Ordered into Active Service (Florida Statute 250.482)
Requests without documentation will not be accepted. Requests for a late withdrawal simply for not
succeeding in a course does not meet the criteria above and will not be approved.
Attitude:
UWF respects the right of instructors to teach and students to learn. The Student Code of Conduct sets forth the
rules, regulations and expected behavior of students enrolled at the University of West Florida. Violations of any
rules, regulations, or behavioral expectations may result in a charge of violating the Student Code of Conduct. It is
the student’s responsibility to read the Student Code of Conduct and conduct themselves accordingly. You may
access the current Student Code of Conduct at http://www.uwf.edu/judicialaffairs.
 Please do not walk into class or walk out of class while the class is in session. Doing so is
a distraction and a discourtesy to the teacher and the other students.
 There will be NO eating, drinking or unnecessary talking while the class is in progress.
 Cell phones must be turned off or set to silent mode.
Expectations for Academic Conduct/Plagiarism Policy:
As members of the University of West Florida, we commit ourselves to honesty. As we strive for
excellence in performance, integrity—personal and institutional—is our most precious asset. Honesty in
our academic work is vital, and we will not knowingly act in ways which erode that integrity. Accordingly,
we pledge not to cheat, nor to tolerate cheating, nor to plagiarize the work of others. We pledge to share
community resources in ways that are responsible and that comply with established policies of fairness.
Cooperation and competition are means to high achievement and are encouraged. Indeed, cooperation is
expected unless our directive is to individual performance. We will compete constructively and
professionally for the purpose of stimulating high performance standards. Finally, we accept adherence to
this set of expectations for academic conduct as a condition of membership in the UWF academic
community.
Assistance:
Students with special needs who require specific examination-related or other course-related
accommodations should contact Barbara Fitzpatrick, Director of Disabled Student Services (DSS),
dss@uwf.edu, (850) 474-2387. DSS will provide the student with a letter for the instructor that will specify
any recommended accommodations.
Weather Emergency Information:
In the case of severe weather or other emergency, the campus might be closed and classes cancelled.
Official closures and delays are announced on the UWF website and broadcast on WUWF-FM.
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WUWF-FM (88.1MHz) is the official information source for the university. Any pertinent
information regarding closings, cancellations, and the re-opening of campus will be broadcast.
In the event that hurricane preparation procedures are initiated, the UWF Home Web Page and
Argus will both provide current information regarding hurricane preparation procedures, the status
of classes and the closing of the university.
Emergency plans for the University of West Florida related to inclement weather are available on the
following UWF web pages:
Information about hurricane preparedness plans is available on the UWF web site:
http://uwfemergency.org/hurricaneprep.cfm
Information about other emergency procedures is available on the UWF web site:
http://uwfemergency.org/