On the roots of hypergraph chromatic polynomials

Sukhada Fadnavis

paper

On the roots of hypergraph chromatic polynomials

arXiv:1509.05950

Abstract

Let $G = (V, E)$ be a finite, simple, connected graph with chromatic polynomial $P_{G} (q)$ . Sokal \cite{sokal} proved that the roots of the chromatic polynomial of $G$ are bounded in absolute value by $K D$ where, $D$ is the maximum degree of the graph and $7 < K < 8$ is a constant. In this paper we generalize this result to uniform hypergraphs. To prove our results we will use the theory of the bounded exponential type graph polynomials.