{"paper":{"title":"Solution to a problem on hamiltonicity of graphs under Ore- and Fan-type heavy subgraph conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning, Shenggui Zhang","submitted_at":"2014-09-11T05:02:22Z","abstract_excerpt":"A graph $G$ is called \\emph{claw-o-heavy} if every induced claw ($K_{1,3}$) of $G$ has two end-vertices with degree sum at least $|V(G)|$ in $G$. For a given graph $R$, $G$ is called \\emph{$R$-f-heavy} if for every induced subgraph $H$ of $G$ isomorphic to $R$ and every pair of vertices $u,v\\in V(H)$ with $d_H(u,v)=2$, there holds $\\max\\{d(u),d(v)\\}\\geq |V(G)|/2$. In this paper, we prove that every 2-connected claw-\\emph{o}-heavy and $Z_3$-\\emph{f}-heavy graph is hamiltonian (with two exceptional graphs), where $Z_3$ is the graph obtained from identifying one end-vertex of $P_4$ (a path with 4"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3325","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"}