Let $G_n$ be a random geometric graph, and then for $q,p \in [0,1)$ we construct a "$(q,p)$-perturbed noisy random geometric graph" $G_n^{ q,p}$ 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 $\omega\left(G_n^{ q,p}\right)$ for several regimes of parameter.
Categories: math.CO math.PR