Georgia Institute of Technology College of Sciences

In this talk, we will discuss the main results of our paper, Counting Colorings of Triangle-Free Graphs, in which we prove the Johansson-Molloy theorem for the upper bound on the chromatic number of a triangle free graph using a novel counting approach developed by Matthieu Rosenfeld, and also extend this result to obtain a lower bound on the number of proper q-colorings for a triangle free graph.  The talk will go over the history of the problem, an outline of our approach, and a high-level sketch of the main proofs. This is joint work with Anton Bernshteyn, Tyler Brazelton, and Akum Kang.