{"paper":{"title":"Orthogonal polarity graphs and Sidon sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Michael Tait","submitted_at":"2014-03-18T15:00:14Z","abstract_excerpt":"Determining the maximum number of edges in an $n$-vertex $C_4$-free graph is a well-studied problem that dates back to a paper of Erd\\H{o}s from 1938. One of the most important families of $C_4$-free graphs are the Erd\\H{o}s-R\\'enyi orthogonal polarity graphs. We show that the Cayley sum graph constructed using a Bose-Chowla Sidon set is isomorphic to a large induced subgraph of the Erd\\H{o}s-R\\'enyi orthogonal polarity graph. Using this isomorphism we prove that the Petersen graph is a subgraph of every sufficiently large Erd\\H{o}s-R\\'enyi orthogonal polarity graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4489","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"}