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For $n \\geq 2k+1$, let $E^k_n=K_{k}\\vee (kK_1+K_{n-2k})$, where \"$\\vee$\" is the \"join\" operation. One can observe $e(E^k_n)=\\binom{n-k}{2}+k^2$ and $E^k_n$ is not Hamiltonian. As $E^k_n$ contains induced claws for $k\\geq 2$, a natural question is to characterize all 2-connected claw-free non-Hamiltonian graph"},"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":"1504.04195","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-16T11:58:17Z","cross_cats_sorted":[],"title_canon_sha256":"117d33e9fb517e7613fc0bf0ab41c27996e3562508a16e9861afbbb126bd8af9","abstract_canon_sha256":"172f3958004ea6e0179054fd081c1a9f06df4209207ffa76382c2346d0b928f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:48.328701Z","signature_b64":"U3EOIrSH9A5GHrwIdjtE9g0bY+l5DN5WDm20hZ91kWqyKt0E7XuCJbP3f0Jk/gxT6AIwSqrKG3ip12kGTzSDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a45b87dacdbb5af320aabf168eb05b7c9b7f03adcacda0dd568d0d72693776c","last_reissued_at":"2026-05-18T00:10:48.328151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:48.328151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal problems on the Hamiltonicity of claw-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning, Xing Peng","submitted_at":"2015-04-16T11:58:17Z","abstract_excerpt":"In 1962, Erd\\H{o}s proved that if a graph $G$ with $n$ vertices satisfies $$ e(G)>\\max\\left\\{\\binom{n-k}{2}+k^2,\\binom{\\lceil(n+1)/2\\rceil}{2}+\\left\\lfloor \\frac{n-1}{2}\\right\\rfloor^2\\right\\}, $$ where the minimum degree $\\delta(G)\\geq k$ and $1\\leq k\\leq(n-1)/2$, then it is Hamiltonian. For $n \\geq 2k+1$, let $E^k_n=K_{k}\\vee (kK_1+K_{n-2k})$, where \"$\\vee$\" is the \"join\" operation. One can observe $e(E^k_n)=\\binom{n-k}{2}+k^2$ and $E^k_n$ is not Hamiltonian. As $E^k_n$ contains induced claws for $k\\geq 2$, a natural question is to characterize all 2-connected claw-free non-Hamiltonian graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04195","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.04195","created_at":"2026-05-18T00:10:48.328243+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04195v3","created_at":"2026-05-18T00:10:48.328243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04195","created_at":"2026-05-18T00:10:48.328243+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJC3Q7NM3O22","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJC3Q7NM3O226MQK","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJC3Q7NM","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7","json":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7.json","graph_json":"https://pith.science/api/pith-number/PJC3Q7NM3O226MQKVPYWR2YFW7/graph.json","events_json":"https://pith.science/api/pith-number/PJC3Q7NM3O226MQKVPYWR2YFW7/events.json","paper":"https://pith.science/paper/PJC3Q7NM"},"agent_actions":{"view_html":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7","download_json":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7.json","view_paper":"https://pith.science/paper/PJC3Q7NM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04195&json=true","fetch_graph":"https://pith.science/api/pith-number/PJC3Q7NM3O226MQKVPYWR2YFW7/graph.json","fetch_events":"https://pith.science/api/pith-number/PJC3Q7NM3O226MQKVPYWR2YFW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7/action/storage_attestation","attest_author":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7/action/author_attestation","sign_citation":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7/action/citation_signature","submit_replication":"https://pith.science/pith/PJC3Q7NM3O226MQKVPYWR2YFW7/action/replication_record"}},"created_at":"2026-05-18T00:10:48.328243+00:00","updated_at":"2026-05-18T00:10:48.328243+00:00"}