COURSE SYLLABUS
Course Prefix/Number: MAD 4301/MAD 5305
Course Title: Graphs and their Applications
Course Credit Hours: 3
Instructor Name and Contact Information:
Dr. Jaromy Kuhl
Room 133, Bldg. 38, Ext. 7702
E-mail: jkuhl@uwf.edu
Prerequisites or Co-Requisites: Pre/Co requisites: Set Theory and Mathematical Logic (MHF 3202)
Course Description:
This course is devoted to graphs and the various ways in which they are used to model certain problems.
In particular, we will study some useful structures found in graphs such as Hamiltonian cycles, matchings,
and subdivisions and we will study some useful invariants for graphs 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.
 Explain the concepts of vertex and edge colorings and prove Vizing’s theorem and Brook’s
theorem.
 Explain the concepts of 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
 Graphs with names
 Vertex degrees
 Paths and Cycles
 Isomorphisms
2. Transportation problems
 Konigsberg bridge problem
 Euler circuits and walks
 Traveling salesman problem
 Hamiltonian cycles in graphs
 Longest cycles in graphs
3. Party problems
 Assignment problems
 Maximum matchings
 Hall’s theorem
 The Gale-Shapely algorithm for stable matchings
 Friendship/stranger problems
 Ramsey numbers
4. Connection problems
 Vertex edge connectivity
 Blocks of a graph
 k-connected graphs
 Menger’s theorem
5. Scheduling problems
 Vertex colorings
 Vizing’s theorem
 Edge colorings
 Brook’s theorem
 Latin Squares
6. Planar Graphs
 The three houses and three utilities problem
 Euler’s formula
 Kuratowki’s Theorem
 The five color theorem for planar graphs
Required texts:
Introductory Graph Theory, Gary Chartrand
Grading / Evaluation:
There will be
 Three in-class tests (inclusive of final exam) each worth 100 points. (undergraduate and graduate
students)
 Four projects. (graduate students)
 Eight to ten homework assignments. (undergraduate and graduate students)
For undergraduate students: Each test is 25% and the homework assignments are for a total of 25%.
For graduate students: Each test is 20%, the four projects are each 5% for a total of 20%, and the
homework assignments are for a total of 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 10, 2:30 – 5:00 p.m.
Classes have been suspend for Labor Day (9/7/2009), Veteran’s Day (11/2/2009), and Thanksgiving
(11/26/2009 – 11/27/2009).
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 class. By
the end of the semester I will expect you to have a high level of familiarity with the subject matter and to
ensure that you attain this…come to class. However, if you need to miss class I understand. You should
get the lecture notes missed from a classmate and arrange a time with me to complete any missed
projects and if you still need assistance 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. No texting.
Examinations:
You will be given 3 exams. You should not miss these unless you have a doctor’s note telling your
sickness, a death in the family, or a university function you cannot miss. Only under these circumstances
will you be allowed to replace your missed test with the score on your final examination. For neatness
sake, bring a pencil and a blue\green book to each test.
The first examination and the final examination will be proctored. Elluminate students will need to either
attend class face-to-face for these exams or find a testing center that will proctor their exam (you will need
to have your proctor approved by me). Most community colleges and universities have testing centers.
The second examination will be take-home and will be administered through eLearning.
Homework:
Each week, except for test week, homework problems will be assigned. Students will be given one week
to complete the assignment. All homework assignments must be turned in via eLearning.
Projects:
Graduate students will be required to complete four assignments. These 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: 10:00 – 12:00 pm MW and 1:00 – 2:00 pm TTh
Withdrawal deadlines:
1. Withdrawal deadline for all courses for the term with partial refund and grade of WR is
September 21st
2. Withdrawal deadline for individual or all courses for the term with an automatic W is November
2nd
3. Withdrawal deadline for all courses for the term with grade of W or WF at the instructor’s
discretion is December 4th
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.
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/