{"paper":{"title":"Turan numbers for bipartite graphs plus an odd cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Jacques Verstraete, Peter Allen, Peter Keevash","submitted_at":"2012-10-14T15:38:38Z","abstract_excerpt":"For an odd integer $k$, let $\\mathcal{C}_k = \\{C_3,C_5,...,C_k\\}$ denote the family of all odd cycles of length at most $k$ and let $\\mathcal{C}$ denote the family of all odd cycles. Erd\\H{o}s and Simonovits \\cite{ESi1} conjectured that for every family $\\mathcal{F}$ of bipartite graphs, there exists $k$ such that $\\ex{n}{\\mathcal{F} \\cup \\mathcal{C}_k} \\sim \\ex{n}{\\mathcal{F} \\cup \\mathcal{C}}$ as $n \\rightarrow \\infty$. This conjecture was proved by Erd\\H{o}s and Simonovits when $\\mathcal{F} = \\{C_4\\}$, and for certain families of even cycles in \\cite{KSV}. In this paper, we give a general a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3805","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"}