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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.3325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-11T05:02:22Z","cross_cats_sorted":[],"title_canon_sha256":"3277b0a25153d172d2e5aa3e04c01691172528e663e56e9c961f622f3461f0c6","abstract_canon_sha256":"b9095f4f168a9cbc80d68a13c0270dc6092dbea8e3809e5ae1b051347679c0b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:57.937236Z","signature_b64":"8CGq9+rGgz1F/dBvVDBhne9t+/ghPD91KG2ltzpgYaPjzQWn40BhKbhvzsiqvC2YP3qADX9TQSutr/h1X+qNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5179337e698169504d24b7e75bb8bff6d3c3b8c4ee71cdeb71bee23dfd6e1ddd","last_reissued_at":"2026-05-18T01:11:57.936882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:57.936882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $G$. 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