Chromatic Number of Random Signed Graphs

Abstract

We naturally extend Bollobas's classical method and result about the chromatic number of random graphs chi(G(n,p)) ~ n/log_b(n) (for p constant, b=1/(1-p)) to the chromatic number of random signed graphs to obtain chi(G(n,p,q)) ~ n/log_b(n) (for p constant, b=1/(1-p), q=o(1)). We also give a sufficient bound on q under which a.a.s. the chromatic number of G(n,p,q) is unchanged before and after adding negative edges.