Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MATH 800 G100

Mathematics: Selected Topics (4)

Class Number: 5978

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Wed, Fri, 12:30–2:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 17, 2025
    Thu, 11:59–11:59 p.m.
    Burnaby

Description

COURSE DETAILS:

Modern structural graph theory builds on classical results about planar graphs and the methods developed for proving the 4-Color Theorem. Some of its main subareas concern perfect graphs, graphs on surfaces and the theory of graph minors.

The course will provide an introduction to different aspects of structural graph theory, including some recent developments. It will be based on a forthcoming monograph prepared jointly by David Wood (Monash University) and the instructor. It will start with classical topics about perfect graphs, planar graphs, graphs on surfaces, graph minors, substructures in sparse and dense graphs, and will end with the recent work on product structure theorems. Time permitting, the course will also cover important use of Szemeredi Regularity Lemma and its relation to the structure of dense graphs.


Prerequisites:
Undergraduate course in graph theory



Course outline:

I.
Connectivity
Menger's Theorem
Disjoint paths problem
Linkages

II.
Perfect graphs
Interval graphs
Chordal graphs
Perfect Graph Theorem
Lovasz Theta-function
chi-boundedness

III.
Treewidth
Series-parallel graphs
Separators
Tree minor theorem

IV.
Planar and outerplanar graphs
Kuratowski Theorem and its consequences
Graph coloring problems on planar graphs
Discharging method
Product structure theorem

V.
Advanced results on treewidth
Brambles and tangles
Grid minor theorem
Erdos-Posa property

VI.
Graphs on surfaces
Combinatorial description of 2-cell embeddings
Forbidden minor characterizations
Coarse geometry of graphs

VII.
Excluded minor structure theorem
Basic version
Product structure theorems

VIII.
Structure of dense graphs
Szemeredi Regularity Lemma and its consequences
Graph limits

Grading

  • Homework Assignments 30%
  • Midterm 30%
  • Final Exam 40%

Materials

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 term 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.