{"paper":{"title":"On a conjecture of Erdos and Simonovits: Even Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Jacques Verstraete, Peter Keevash","submitted_at":"2011-07-23T22:42:15Z","abstract_excerpt":"Let $\\mc{F}$ be a family of graphs. A graph is {\\em $\\mc{F}$-free} if it contains no copy of a graph in $\\mc{F}$ as a subgraph. A cornerstone of extremal graph theory is the study of the {\\em Tur\\'an number} $ex(n,\\mc{F})$, the maximum number of edges in an $\\mc{F}$-free graph on $n$ vertices. Define the {\\em Zarankiewicz number} $z(n,\\mc{F})$ to be the maximum number of edges in an $\\mc{F}$-free {\\em bipartite} graph on $n$ vertices. Let $C_k$ denote a cycle of length $k$, and let $\\mc{C}_k$ denote the set of cycles $C_{\\ell}$, where $3 \\le \\ell \\leq k$ and $\\ell$ and $k$ have the same parity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4715","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"}