"The Coloring Graph and variations"

Document Type

Presentation Abstract

5-19-2010

Abstract

Proper colorings of a graph have been studied from many angles. While it is sometimes important to find just one coloring of a graph that uses a minimum number of colors, it can also be of interest to consider all the ways to properly color a graph using a certain number of colors. One way to do this is with a Coloring Graph. Given a graph G, the Coloring Graph C(G) has vertex set the set of all colorings of the graph G. The edge set can be defined in various ways for instance, there is an edge between two colorings if they are identical on V(Gx) for some xV (G). Another possibility would be to consider colorings to be adjacent if a Kempe chain takes you from one to the other.

In this talk we give an overview of various kinds of coloring graphs and then focus on the Cannonical coloring graph where only nonisomorphic colorings of the graph G are used as vertices. The representative of each set of isomorphic colorings are chosen according to a canonical ordering.