On the chromatic forcing number of a random graph

Abstract

When we wish to compute lower bounds for the chromatic number χ( G) of a graph G, it is of interest to know something about the ‘chromatic forcing number’ f χ ( G), which is defined to be the least number of vertices in a subgraph H of G such that χ( H) = χ( G). We show here that for random graphs G n,p with n vertices, f χ ( G n, p ) is almost surely at least ( 1 2 −ε) n, despite say the fact that the largest complete subgraph of G n,p has only about log n vertices.