McKay, Ghislain2018-09-252018-09-252018-09-252018-09-21http://hdl.handle.net/10012/13924In1993 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.enGraph TheoryChromatic PolynomialsCorrelation InequalityMaster Thesis