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2006 Broken-Cycle-Free Subgraphs and the Log-Concavity Conjecture for Chromatic Polynomials
P. H. Lundow, K. Markström
Experiment. Math. 15(3): 343-354 (2006).

Abstract

This paper concerns the coefficients of the chromatic polynomial of a graph. We first report on a computational verification of the strict log-concavity conjecture for chromatic polynomials for all graphs on at most $11$ vertices, as well as for certain cubic graphs.

In the second part of the paper we give a number of conjectures and theorems regarding the behavior of the coefficients of the chromatic polynomial, in part motivated by our computations. Here our focus is on $\varepsilon(G)$, the average size of a broken-cycle-free subgraph of the graph $G$, whose behavior under edge deletion and contraction is studied.

Citation

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P. H. Lundow. K. Markström. "Broken-Cycle-Free Subgraphs and the Log-Concavity Conjecture for Chromatic Polynomials." Experiment. Math. 15 (3) 343 - 354, 2006.

Information

Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1120.05032
MathSciNet: MR2264471

Subjects:
Primary: 05C15

Keywords: chromatic polynomial , Log-concavity , subgraphs

Rights: Copyright © 2006 A K Peters, Ltd.

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Vol.15 • No. 3 • 2006
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