The degree chromatic polynomial Pm(G,k) of a graph G counts the number of k-colorings in which no vertex has m adjacent vertices of its same color. We prove Humpert and Martin's conjecture on the leading terms of the degree chromatic polynomial of a tree.

Author Bio

Diego Cifuentes is a double major in Mathematics and Electronics Engineering at Universidad de los Andes in Colombia and will be graduating in September of 2012. The paper 㤼㸳On the degree-chromatic polynomial of a tree” began after a course in Discrete Geometry with Prof. Federico Ardila. A couple of weeks after the end of the course, Federico presented to the class a recent conjecture stated by Humpert and Martin. Diego solved the problem in the following weeks. He is currently doing his undergraduate thesis in Algebraic combinatorics with Federico. Diego hopes to enter a Ph.D. program in Mathematics.