{"paper":{"title":"Extensions of 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":"2017-03-29T23:28:47Z","abstract_excerpt":"Let $n, d$ be integers with $1 \\leq d \\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, and set $h(n,d):={n-d \\choose 2} + d^2$. Erd\\H{o}s proved that when $n \\geq 6d$, each nonhamiltonian graph $G$ on $n$ vertices with minimum degree $\\delta(G) \\geq d$ has at most $h(n,d)$ edges. He also provides a sharpness example $H_{n,d}$ for all such pairs $n,d$. Previously, we showed a stability version of this result: for $n$ large enough, every nonhamiltonian graph $G$ on $n$ vertices with $\\delta(G) \\geq d$ and more than $h(n,d+1)$ edges is a subgraph of $H_{n,d}$.\n  In this paper, we show that not o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10268","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"}