{"paper":{"title":"The maximum number of cliques in a graph embedded in a surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David R. Wood, Ga\\v{s}per Fijav\\v{z}, Gwena\\\"el Joret, Thom Sulanke, Vida Dujmovi\\'c","submitted_at":"2009-06-22T23:01:30Z","abstract_excerpt":"This paper studies the following question: Given a surface $\\Sigma$ and an integer $n$, what is the maximum number of cliques in an $n$-vertex graph embeddable in $\\Sigma$? We characterise the extremal graphs for this question, and prove that the answer is between $8(n-\\omega)+2^{\\omega}$ and $8n+{3/2} 2^{\\omega}+o(2^{\\omega})$, where $\\omega$ is the maximum integer such that the complete graph $K_\\omega$ embeds in $\\Sigma$. For the surfaces $\\mathbb{S}_0$, $\\mathbb{S}_1$, $\\mathbb{S}_2$, $\\mathbb{N}_1$, $\\mathbb{N}_2$, $\\mathbb{N}_3$ and $\\mathbb{N}_4$ we establish an exact answer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4142","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"}