{"paper":{"title":"An Ore-type condition for existence of two disjoint cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianguo Qian, Maoqun Wang","submitted_at":"2019-05-01T09:52:56Z","abstract_excerpt":"Let $n_{1}$ and $n_{2}$ be two integers with $n_{1},n_{2}\\geq3$ and $G$ a graph of order $n=n_{1}+n_{2}$. As a generalization of Ore's degree condition for the existence of Hamilton cycle in $G$, El-Zahar proved that if $\\delta(G)\\geq \\left\\lceil\\frac{n_{1}}{2}\\right\\rceil+\\left\\lceil\\frac{n_{2}}{2}\\right\\rceil$ then $G$ contains two disjoint cycles of length $n_{1}$ and $n_{2}$. Recently, Yan et. al considered the problem by extending the degree condition to degree sum condition and proved that if $d(u)+d(v)\\geq n+4$ for any pair of non-adjacent vertices $u$ and $v$ of $G$, then $G$ contains "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00239","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"}