English

On the clique number of noisy random geometric graphs

Combinatorics 2022-08-24 v1 Probability

Abstract

Let GnG_n be a random geometric graph, and then for q,p[0,1)q,p \in [0,1) we construct a "(q,p)(q,p)-perturbed noisy random geometric graph" Gnq,pG_n^{q,p} where each existing edge in GnG_n is removed with probability qq, while and each non-existent edge in GnG_n is inserted with probability pp. We give asymptotically tight bounds on the clique number ω(Gnq,p)\omega\left(G_n^{q,p}\right) for several regimes of parameter.

Keywords

Cite

@article{arxiv.2208.10558,
  title  = {On the clique number of noisy random geometric graphs},
  author = {Matthew Kahle and Minghao Tian and Yusu Wang},
  journal= {arXiv preprint arXiv:2208.10558},
  year   = {2022}
}

Comments

34 pages, 4 figures