Expansions of chromatic polynomials and log-concavity

Brenti, Francesco

doi:10.1090/S0002-9947-1992-1069745-7

Expansions of chromatic polynomials and log-concavity
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by Francesco Brenti

Trans. Amer. Math. Soc. 332 (1992), 729-756

DOI: https://doi.org/10.1090/S0002-9947-1992-1069745-7

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Abstract:

In this paper we present several results and open problems about logconcavity properties of sequences associated with graph colorings. Five polynomials intimately related to the chromatic polynomial of a graph are introduced and their zeros, combinatorial and log-concavity properties are studied. Four of these polynomials have never been considered before in the literature and some yield new expansions for the chromatic polynomial.

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