Simon Fraser University
Engaging the World

Course Outlines

Spring 2023 - MATH 745 G100

Graph Theory (3)

Class Number: 5322

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 4 – Apr 11, 2023: Mon, Wed, Fri, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 22, 2023
    Sat, 3:30–6:30 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Graph coloring, Hamiltonian graphs, planar graphs, random graphs, Ramsey theory, extremal problems, additional topics. Students may not take a 700-division course if it is being offered in conjunction with a 400-division course which they have taken previously.

COURSE DETAILS:

This is a continuation of MATH 345, where the student will learn more advanced materials. Essentially, we will cover Chapter 5, 6, 7 and a part of 8 (as time and interest permits) of the textbook.

V. Graph Colourings:

  • Upper bounds for Chromatic number
  • Structure of k-chromatic graphs
  • Enumerative aspects

VI. Graph Embeddings

  • Euler's Formula
  • Characterization of planar graphs
  • Parameters of embeddings
VII. Edges and Cycles
  • Line graphs
  • Edge colouring
  • Hamiltonian cycles
  • Planarity and cycles

VIII. Additional Topics. Depending on time and interest, some of the following topics will be studied:

  • Ramsey Theory
  • Extremal Problems
  • Random Graphs
  • Eigenvalues of Graphs

Grading

  • Homework Assignments and In-class Presentation 30%
  • Midterm/Project 30%
  • Final Exam 40%

NOTES:

 

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.

Materials

MATERIALS + SUPPLIES:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings,
this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable
internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in
a computer is sufficient).

RECOMMENDED READING:

Introduction to Graph Theory by Douglas B. West will be on reserve at the SFU Burnaby library.

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html