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In this paper, we introduce a new concept, and say that $G$ is \\emph{$S$-c-heavy} if for a given graph $S$ and every induced subgraph $G'$ of $G$ isomorphic to $S$ and every maximal clique $C$ of $G'$, every non-trivial component of $G'-C$ contains a vertex"},"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":"1506.02795","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T06:36:54Z","cross_cats_sorted":[],"title_canon_sha256":"d24332f43af61efb9839e4b58e18fa40a8e0023b9d376bd46a2bd18bc86626fb","abstract_canon_sha256":"a6e35059480670ce8c779f027e58fdd5506b1ae1b1f01dc3702f399583a94ab7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:13.602207Z","signature_b64":"/ytD3gQySd0HGmzGLVX13ucV6DAOPM+xn0Ya0X8Vx53A538eo32P3BuM76cTe282VAhYa+A1p/eIzqb5P9cjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"762b2d04f5f6c43b066b890025a0e8a66d3087932ed5fd3c64b13db024145b0a","last_reissued_at":"2026-05-18T00:42:13.601614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:13.601614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heavy subgraphs, stability and hamiltonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning","submitted_at":"2015-06-09T06:36:54Z","abstract_excerpt":"Let $G$ be a graph. 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