Graphs and Matroids Seminar - Dao Chen Yuan

Title: Chromatic Number of Random Signed Graphs

Abstract: A signed graph is a graph where edges are labelled {+1,-1}. A signed colouring in 2k colours maps the vertices of a signed graph to {-k,...,-1,1,...,k}, such that neighbours joined by a positive edge do not share the same colour, and those joined by a negative edge do not share opposite colours. It is a classical result that the chromatic number of a G(n,p) Erdos-Renyi random graph is asymptotically almost surely n/(2log_b(n)), where p is constant and b=1/(1-p). We extend the method used there to prove that the chromatic number of a G(n,p,q) random signed graph, where q is the probability that an edge is labelled -1, is also a.a.s. n/(2log_b(n)), if p is constant and q=o(1).