Fall 2019 - MATH 820 G100
Graph Theory (4)
Class Number: 4130
Delivery Method: In Person
Algebraic graph theory, extremal graph theory, coloring problems, path and cycle structure of graphs, application of graphs, hypergraphs, and current research topics.
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.
- Homework (5-6 equally weighted assignments) 40%
- Final Take-Home Exam 60%
Note: MATH 820 classes will start in the second week of the semester.
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.
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.
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ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS