Results on Chromatic Polynomials Inspired by a Correlation Inequality of G.E. Farr
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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Ghislain McKay
(2018).
Results on Chromatic Polynomials Inspired by a Correlation Inequality of G.E. Farr. UWSpace.
http://hdl.handle.net/10012/13924
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