MA 715, Graph Theory.

This is an introductory course in graph theory. The course will cover all the basic concepts and results in the field, such as: Eulerian and Hamiltonian graphs, spanning trees (Cayley's formula), matchings (Hall's Theorem, Konig's Theorem), connectivity (Menger's Theorem), vertex colorings (Brook's Theorem), edge colorings (Vizing's Theorem) and planar graphs (Kuratowski's Theorem). Time premitting we will cover some of the results on perfect graphs as well. Although there are a lot of important applications of graph theory (some of which are seen in MA 618), this course will focus on understanding the structure of graphs and the techniques used to analyze problems in graph theory.

Text: Introduction to Graph Theory, D. West, Prentice-Hall, 2001. ISBN: 0-13-014400-2.