{"paper":{"title":"Triangle-free induced subgraphs of polarity graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Jared Loucks","submitted_at":"2017-03-18T20:28:27Z","abstract_excerpt":"Given a finite projective plane $\\Pi$ and a polarity $\\theta$ of $\\Pi$, the corresponding polarity graph is the graph whose vertices are the points of $\\Pi$. Two distinct vertices $p$ and $p'$ are adjacent if $p$ is incident to $\\theta (p')$. Polarity graphs have been used in a variety of extremal problems, perhaps the most well-known being the Tur\\'{a}n number of the cycle of length four. We investigate the problem of finding the maximum number of vertices in an induced triangle-free subgraph of a polarity graph. Mubayi and Williford showed that when $\\Pi$ is the projective geometry $PG(2,q)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06347","kind":"arxiv","version":2},"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"}