Lon Mitchell

*Galvin's Proof of the Dinitz Conjecture*

**Abstract**. The chromatic number of a graph is the smallest number of colors needed to color every vertex so that adjacent vertices have different colors. A famous open problem in graph theory asks whether the chromatic number of a line graph is always equal to its list-chromatic number. This talk will introduce these concepts and show how Fred Galvin used two well-known theorems to give a proof in a special case.