Math 510
Introduction to Graph Theory
Spring 2014

Syllabus

The textbook is W.T. Tutte, Graph Theory, Cambridge University Press, 1998.

• 1/26 – 2/3
  Introduction to graph theory. (Alex Schaefer)


• 2/5 – 2/26
  Chapter I: Graphs and Subgraphs. (with Vaidy Sivaraman)
  • Description: Basics.


• 2/26 – 3/13
  Chapter II: Contractions and the Theorem of Menger.
  • Description: More basics; and famous theorems.


• 3/13 – 3/21
  Chapter III: 2-Connection.
  • Description: Basic structure theory.


• 3/24 – 4/25
  Chapter IV: 3-Connection.
  • Description: Higher structure theory.


• 5/1 – 5/15
  Chapter IX: Polynomials Associated with Graphs. (with Vaidy Sivaraman)
  • Description: Algebra of deletion-contraction invariants. Chromatic number and chromatic index. Line graph.


• — (no classes on this chapter)
  Chapter VIII: Algebraic Duality.
  • Description: Algebraic approach to graph structure.
  • Read Sects. IX.3, IX.5, and VIII.1 and the first page of Sects. VIII.4–5. Concentrate on the definitions, explanations, and theorems, not the proofs.

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