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arXiv · 1509.05950

On the roots of hypergraph chromatic polynomials

Sukhada Fadnavis
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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 $KD$ 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.

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Sukhada Fadnavis. 2015-09-20. On the roots of hypergraph chromatic polynomials. https://arxiv.org/abs/1509.05950

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