ABSTRACT:
In 1995 Stanley introduced the chromatic symmetric function associated to every simple graph. In this talk, I’ll present a novel technique to write this function as a linear combination of symmetric chromatic functions for smaller graphs. I will give two applications of this technique, the first is a sufficient condition for two graphs to have the same chromatic symmetric function; and the second is a construction of pairs of unicyclic graphs with the same symmetric
chromatic function.
In addition, I will discuss some progress on the question of whether it is possible to determine a tree from its chromatic symmetric function.