## Experimental Mathematics

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

#### 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

https://projecteuclid.org/euclid.em/1175789763

Mathematical Reviews number (MathSciNet)
MR2264471

Zentralblatt MATH identifier
1120.05032

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

#### 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