{"paper":{"title":"On the independence number of graphs related to a polarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francesco Pavese, Leo Storme, Sam Mattheus","submitted_at":"2017-04-03T09:17:47Z","abstract_excerpt":"We investigate the independence number of two graphs constructed from a polarity of $\\mathrm{PG}(2,q)$. For the first graph under consideration, the Erd\\H{o}s-R\\'enyi graph $ER_q$, we provide an improvement on the known lower bounds on its independence number. In the second part of the paper we consider the Erd\\H{o}s-R\\'enyi hypergraph of triangles $\\mathcal{H}_q$. We determine the exact magnitude of the independence number of $\\mathcal{H}_q$, $q$ even. This solves a problem posed by Mubayi and Williford."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00487","kind":"arxiv","version":1},"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"}