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Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs
Citation
Dong, F. (2017). Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs. European Journal of Combinatorics, 64, 138-151. https://doi.org/10.1016/j.ejc.2017.04.006
Abstract
In this paper, we present some properties on chromatic polynomials of hypergraphs which do not hold for chromatic polynomials of graphs. We first show that chromatic polynomials of hypergraphs have all integers as their zeros and contain dense real zeros in the set of real numbers. We then prove that for any multigraph G = (V, E), the number of totally cyclic orientations of G is equal to the value of IP(HG,-1)I, where P(HG, λ) is the chromatic polynomial of a hypergraph HG which is constructed from G. Finally we show that the multiplicity of root "O" of P(H, λ) may be at least 2 for some connected hypergraphs H, and the multiplicity of root "1" of P(H, λ) may be 1 for some connected and separable hypergraphs H and may be 2 for some connected and non-separable hypergraphs H.
Date Issued
2017
Publisher
Elsevier
Journal
European Journal of Combinatorics