Simon Fraser University
Engaging the World

Course Outlines

Fall 2023 - MATH 820 G100

Graph Theory (4)

Class Number: 2125

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 6 – Dec 5, 2023: Wed, Fri, 2:30–4:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Algebraic graph theory, extremal graph theory, coloring problems, path and cycle structure of graphs, application of graphs, hypergraphs, and current research topics.

COURSE DETAILS:

I. Matchings (Matchings in bipartite graphs. Matchings in general graphs. Tutte theorem. Erdos-Posa Theorem. Path covers)  

II. Connectivity (Menger’s Theorem. Mader’s Theorem. Linkages)  

III. Planar Graphs and graphs on other surfaces  

IV. Colorings and Nowhere-Zero Flows (Planar graphs. Coloring-flow duality. Cycle Double Cover Conjecture. List Coloring)  

V. Substructures in Dense Graphs (Extremal graph theory. Regularity Lemma and its Applications. Erdős-Stone theorem)  

VI. Substructures in Sparse Graphs (Minors and topological minors. Immersions. Bollobás-Thomason, Komlós-Szeméredi Theorem. Hadwiger’s conjecture. Excluded Minor Theorem)

VII. Other topics from the textbook or from selected papers on some recent advances in graph theory.

Grading

  • Assignments 5-6 (equally weighted) 20%
  • Presentations 1-2 30%
  • Final project/exam (take home) 50%

NOTES:

Note: MATH 820 classes will start in the second week of the semester.

Materials

REQUIRED READING:

1. R. Diestel: Graph Theory – 5th ed., Springer-Verlag, 2017. (Electronic copy is available for course use through the SFU Library.)

2. Selected papers concerning the topics of the course.

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

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the semester are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.