{"paper":{"title":"Local cliques in ER-perturbed random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Matthew Kahle, Minghao Tian, Yusu Wang","submitted_at":"2018-10-19T07:56:04Z","abstract_excerpt":"Random graphs are mathematical models that have applications in a wide range of domains. We study the following model where one adds Erd\\H{o}s--R\\'enyi (ER) type perturbation to a random geometric graph. More precisely, assume $G_\\mathcal{X}^{*}$ is a random geometric graph sampled from a nice measure on a metric space $\\mathcal{X} = (X,d)$. The input observed graph $\\widehat{G}(p,q)$ is generated by removing each existing edge from $G_\\mathcal{X}^*$ with probability $p$, while inserting each non-existent edge to $G_\\mathcal{X}^{*}$ with probability $q$. We refer to such random $p$-deletion an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08383","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}