Simon Fraser University
Engaging the World

Course Outlines

Spring 2023 - MATH 445 D100

Graph Theory (3)

Class Number: 5272

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

  • Prerequisites:

    MATH 345 with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

Graph coloring, Hamiltonian graphs, planar graphs, random graphs, Ramsey theory, extremal problems, additional topics. Quantitative.

COURSE DETAILS:

Course Outline:

This is a continuation of MATH 345, where the student will learn more advanced material. Essentially, we will cover Chapters 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: Perfect Graphs, Matroids, Ramsey Theory, Extremal Problems, Random Graphs, Eigenvalues of Graphs.


Note: This is a cross-listed course with MATH 745.

Grading

  • 5 Homeworks: (4% each) (Graduate students will have an extended set of problems.) 20%
  • Midterm 30%
  • Final Exam 50%

NOTES:

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

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester
 

Materials

RECOMMENDED READING:

Introduction to Graph Theory
2nd Edition
Author: DB West
Publisher: Pearson

Note from publisher: there are no differences between the Second Edition and the "Pearson Modern Classic" edition also called "Classic Version." 
ISBN: 9780131437371

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.

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