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Results on Chromatic Polynomials Inspired by a Correlation Inequality of G.E. Farr

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Date

2018-09-25

Authors

McKay, Ghislain

Advisor

Wagner, David

Journal Title

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Publisher

University of Waterloo

Abstract

In1993 Graham Farr gave a proof of a correlation inequality involving colourings of graphs. His work eventually led to a conjecture that number of colourings of a graph with certain properties gave a log-concave sequence. We restate Farr's work in terms of the bivariate chromatic polynomial of Dohmen, Poenitz, Tittman and give a simple, self-contained proof of Farr's inequality using a basic combinatorial approach. We attempt to prove Farr's conjecture through methods in stable polynomials and computational verification, ultimately leading to a stronger conjecture.

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Keywords

Graph Theory, Chromatic Polynomials, Correlation Inequality

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