{"paper":{"title":"The Tur\\'an number of sparse spanning graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Noga Alon, Raphael Yuster","submitted_at":"2014-04-04T08:20:58Z","abstract_excerpt":"For a graph $H$, the {\\em extremal number} $ex(n,H)$ is the maximum number of edges in a graph of order $n$ not containing a subgraph isomorphic to $H$. Let $\\delta(H)>0$ and $\\Delta(H)$ denote the minimum degree and maximum degree of $H$, respectively. We prove that for all $n$ sufficiently large, if $H$ is any graph of order $n$ with $\\Delta(H) \\le \\sqrt{n}/200$, then $ex(n,H)={{n-1} \\choose 2}+\\delta(H)-1$. The condition on the maximum degree is tight up to a constant factor. This generalizes a classical result of Ore for the case $H=C_n$, and resolves, in a strong form, a conjecture of Gle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1182","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"}