On the roots of hypergraph chromatic polynomials

2015/09/20 by Sukhada Fadnavis, Fadnavis, Sukhada
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO

paper · pdf · doi:10.48550/arxiv.1509.05950

arxiv created 2015/09/20 · openalex publication_date 2015/09/20 · arxiv updated 2015/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G = (V,E) be a finite, simple, connected graph with chromatic polynomial P_G(q). Sokal \citesokal 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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