On the Chromatic Number of Random Cayley Graphs

Abstract

Let G be an abelian group of cardinality n, where hcf(n, 6) = 1, and let A be a random subset of G. Form a graph ΓA on vertex set G by joining x to y if and only if x + y ∈ A. Then, with high probability as n → ∞, the chromatic number χ(ΓA) is at most (1+o(1))n/2log2n. This is asymptotically sharp when G = ℤ/nℤ, n prime.