{"paper":{"title":"Infinite Tur\\'an problems for bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Xing Peng","submitted_at":"2013-05-29T20:42:47Z","abstract_excerpt":"We consider an infinite version of the bipartite Tur\\'{a}n problem. Let $G$ be an infinite graph with $V(G) = \\mathbb{N}$ and let $G_n$ be the $n$-vertex subgraph of $G$ induced by the vertices $\\{1,2, \\dots, n \\}$. We show that if $G$ is $K_{2,t+1}$-free then for infinitely many $n$, $e(G_n) \\leq 0.471 \\sqrt{t} n^{3/2}$. Using the $K_{2,t+1}$-free graphs constructed by F\\\"{u}redi, we construct an infinite $K_{2,t+1}$-free graph with $e(G_n) \\geq 0.23 \\sqrt{t}n^{3/2}$ for all $n \\geq n_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6945","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"}