Graph coloring is a main topic in graph theory. Standard questions in
this area ask what the minimum number of required colors to color a
graph in a certain way is. Even though those problems are easy to state
and look simple, most of them are not easy to solve and drive the
development of modern combinatorics. This course will address various
topics in graph coloring and will discuss related methods that are also
used in other areas in combinatorics. Tentative topics include
probabilistic method, Four Color Theorem, Tutte's flow conjectures,
list-coloring, algebraic method, Hadwiger's conjecture, fractional
coloring, topological method, perfect graphs, chi-boundedness.
Prerequisites: Math 613