On the clique number of noisy random geometric graphs

Abstract

Let G n be a random geometric graph, and then for q, p ∈ [0, 1) we construct a (q, p)-perturbed noisy random geometric graph G q,p n where each existing edge in G n is removed with probability q, while and each non-existent edge in G n is inserted with probability p. We give asymptotically tight bounds on the clique number 𝜔 ( G q,p n) for several regimes of parameter.