Math 38: Graph Theory

Spring 2018


Course Description

A graph is a mathematical structure used to model pairwise relations between objects. A "graph" is made up of "vertices" and "edges" that connect the vertices. The first paper on graph theory was published by Euler in 1736 on the seven Bridges of Königsberg.

In this course we will cover the fundamental concepts of Graph Theory: simple graphs, digraphs, Eulerian and Hamiltonian graphs, trees, matchings, networks, paths and cycles, graphs colorings and planar graphs. Famous problems in Graph Theory include: Minimum Connector Problem (building roads at minimum cost), the Marriage Problem (matching men and women into compatible pairs), the Assignment Problem (filling n jobs in the best way), the Network Flow Problem (maximizing flow in a network), the Committee Scheduling Problem (using the fewest time slots), the Four Color Problem (coloring maps with four colors so that adjacent regions have different colors), and the Traveling Salesman Problem (visiting n cities with minimum cost).

Graph theory has many applications to a many other subjects and areas of mathematics, for example, in computer science it can be used to represent networks of communication, data organization, computational device, the flow of computation, etc.

The objectives of the course are:

  • Students will be able to solve problems in graph theory.
  • Students will improve their proof-writing skills.
  • Students will be well-prepared courses in any subjects that use graphs for modeling.
  • "Mathematics is not for spectators; in order to gain in understanding, confidence, and enthusiasm one has to participate." M.A. Armstrong
    DateTime & Location
    Midterm #1 Monday, April 23 6 - 8 PM - KH 006
    Midterm #2 Monday, May 14 6 - 8 PM - KH 006
    Take-Home Final Exam May 30th Due: June 1 at 12 PM

    The course grade will be computed as follows:

    Percent of Final Grade
    Midterms 40 (20 each)
    Homework 20
    Participation 10
    Final Exam 30

    Students will be graded on class participation. Of course it is difficult to participate if one does not come to class at all, and so habitual absence will also be reflected in the class participation grade.
    Homework Policy
    Written homework will be assigned daily and will be collected once a week at the beginning of class.
    • All homework assignments will be posted on the course assignment's webpage.
    • Unexcused late and missing papers count zero.
    • Homework is to be written neatly using both sides of 8 1/2 x 11 inch paper. Do not use paper from a spiral notebook unless you can tear off the ragged edge. All papers are to be stapled.
    • Use English. If you can't read your solutions aloud as fluently as if you were reading a textbook, try using nouns and verbs in your write ups!
    Douglas B. West, Introduction to Graph Theory, Second Edition, Prentice-Hall.
    The home page of the textbook can be found here (Links to an external site.)
    Honor Principle
    Students are encouraged to work together to do homework problems. What is important is a student's eventual understanding of homework problems, and not how that is achieved.

    The honor principle on homework: What a student turns in as a homework solution is to be his or her own understanding of how to do the problem. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. It is a violation of the honor code to copy solutions from problems posted on the web or book or any other source. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Honor Code. For example, it is a breach of the honor code to read the solutions of someone else in order to write your solution.

    The honor principle on exams: Students may not give or receive assistance of any kind on an exam from any person except for the professor or someone explicitly designated by the professor to answer questions about the exam.

    If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me I will be glad to help clarify things. It is always easier to ask beforehand than to have trouble later!
    Disabilities and Religious Observances
    Students with disabilities enrolled in this course and who may need disability-related classroom accommodations are encouraged to make an appointment to see your instructor before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested.

    Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.

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