{"paper":{"title":"A stability version for a theorem of Erd\\H{o}s on nonhamiltonian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Ruth Luo, Zolt\\'an F\\\"uredi","submitted_at":"2016-08-19T21:30:30Z","abstract_excerpt":"Let $n, d$ be integers with $1 \\leq d \\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, and set $h(n,d):={n-d \\choose 2} + d^2$ and $e(n,d):= \\max\\{h(n,d),h(n, \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor)\\}$. Because $h(n,d)$ is quadratic in $d$, there exists a $d_0(n)=(n/6)+O(1)$ such that $e(n,1)> e(n, 2)> \\dots >e(n,d_0)=e(n, d_0+1)=\\dots = e(n,\\left \\lfloor \\frac{n-1}{2} \\right \\rfloor)$. A theorem by Erd\\H{o}s states that for $d\\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, any $n$-vertex nonhamiltonian graph $G$ with minimum degree $\\delta(G) \\geq d$ has at most $e(n,d)$ edges, and for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05741","kind":"arxiv","version":2},"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"}