On the clique number of noisy random geometric graphs

Abstract

Let Gn$$ {G}_n $$ be a random geometric graph, and then for q,p∈[0,1)$$ q,p\in \left[0,1\right) $$ we construct a (q,p)$$ \left(q,p\right) $$ ‐perturbed noisy random geometric graph Gnq,p$$ {G}_n^{q,p} $$ where each existing edge in Gn$$ {G}_n $$ is removed with probability q$$ q $$ , while and each non‐existent edge in Gn$$ {G}_n $$ is inserted with probability p$$ p $$ . We give asymptotically tight bounds on the clique number ωGnq,p$$ \omega \left({G}_n^{q,p}\right) $$ for several regimes of parameter.