On the degree-chromatic polynomial of a tree

preprint2011arXivOpen access

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.

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On the degree-chromatic polynomial of a tree

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