Experimental Mathematics

Broken-Cycle-Free Subgraphs and the Log-Concavity Conjecture for Chromatic Polynomials

P. H. Lundow and K. Markström

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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.

Article information

Source
Experiment. Math., Volume 15, Issue 3 (2006), 343-354.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.em/1175789763

Mathematical Reviews number (MathSciNet)
MR2264471

Zentralblatt MATH identifier
1120.05032

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

Keywords
Chromatic polynomial log-concavity subgraphs

Citation

Lundow, P. H.; Markström, K. Broken-Cycle-Free Subgraphs and the Log-Concavity Conjecture for Chromatic Polynomials. Experiment. Math. 15 (2006), no. 3, 343--354. https://projecteuclid.org/euclid.em/1175789763


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