{"paper":{"title":"Fan-type degree condition restricted to triples of induced subgraphs ensuring Hamiltonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning","submitted_at":"2013-03-09T20:02:25Z","abstract_excerpt":"In 1984, Fan gave a sufficient condition involving maximum degree of every pair of vertices at distance two for a graph to be Hamiltonian. Motivated by Fan's result, we say that an induced subgraph $H$ of a graph $G$ is $f$-heavy if for every pair of vertices $u,v\\in V(H)$, $d_{H}(u,v)=2$ implies that $\\max\\{d(u),d(v)\\}\\geq n/2$. For a given graph $R$, $G$ is called $R$-$f$-heavy if every induced subgraph of $G$ isomorphic to $R$ is $f$-heavy. For a family $\\mathcal{R}$ of graphs, $G$ is $\\mathcal{R}$-$f$-\\emph{heavy} if $G$ is $R$-$f$-heavy for every $R\\in \\mathcal{R}$. In this note we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2263","kind":"arxiv","version":4},"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"}