{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MBE2APQS2XB6L3M6EKBK5LS4GP","short_pith_number":"pith:MBE2APQS","schema_version":"1.0","canonical_sha256":"6049a03e12d5c3e5ed9e2282aeae5c33e3dedd2f4ef641a936059c948aa7914d","source":{"kind":"arxiv","id":"1309.0217","version":6},"attestation_state":"computed","paper":{"title":"Spectral radius and Hamiltonian properties of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Jun Ge","submitted_at":"2013-09-01T13:06:31Z","abstract_excerpt":"Let $G$ be a graph with minimum degree $\\delta$. The spectral radius of $G$, denoted by $\\rho(G)$, is the largest eigenvalue of the adjacency matrix of $G$. In this note we mainly prove the following two results. (1) Let $G$ be a graph on $n\\geq 4$ vertices with $\\delta\\geq 1$. If $\\rho(G)> n-3$, then $G$ contains a Hamilton path unless $G\\in\\{K_1\\vee (K_{n-3}+2K_1),K_2\\vee 4K_1,K_1\\vee (K_{1,3}+K_1)\\}$. (2) Let $G$ be a graph on $n\\geq 14$ vertices with $\\delta \\geq 2$. If $\\rho(G)\\geq \\rho(K_2\\vee (K_{n-4}+2K_1))$, then $G$ contains a Hamilton cycle unless $G= K_2\\vee (K_{n-4}+2K_1)$. As cor"},"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":"1309.0217","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-01T13:06:31Z","cross_cats_sorted":[],"title_canon_sha256":"313385c72b3417ac22d77637638b7efe21f7962afda4060dc31ad85cbb7ead62","abstract_canon_sha256":"57b3cb2efef01d7adfb01864d1c7df27e672479e14ee77d566bc2afbdf5b8ded"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:29.547037Z","signature_b64":"j8B7r8JNWHLABbjuhVd/TCnJU5JPqxCBXN97Sa1s78RqZeea6qM9xDxlWuCH3XO0ZvoIgaHpGXpN7RRDW804Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6049a03e12d5c3e5ed9e2282aeae5c33e3dedd2f4ef641a936059c948aa7914d","last_reissued_at":"2026-05-18T02:27:29.546264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:29.546264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral radius and Hamiltonian properties of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Jun Ge","submitted_at":"2013-09-01T13:06:31Z","abstract_excerpt":"Let $G$ be a graph with minimum degree $\\delta$. The spectral radius of $G$, denoted by $\\rho(G)$, is the largest eigenvalue of the adjacency matrix of $G$. In this note we mainly prove the following two results. (1) Let $G$ be a graph on $n\\geq 4$ vertices with $\\delta\\geq 1$. If $\\rho(G)> n-3$, then $G$ contains a Hamilton path unless $G\\in\\{K_1\\vee (K_{n-3}+2K_1),K_2\\vee 4K_1,K_1\\vee (K_{1,3}+K_1)\\}$. (2) Let $G$ be a graph on $n\\geq 14$ vertices with $\\delta \\geq 2$. If $\\rho(G)\\geq \\rho(K_2\\vee (K_{n-4}+2K_1))$, then $G$ contains a Hamilton cycle unless $G= K_2\\vee (K_{n-4}+2K_1)$. As cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0217","kind":"arxiv","version":6},"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":"1309.0217","created_at":"2026-05-18T02:27:29.546394+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0217v6","created_at":"2026-05-18T02:27:29.546394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0217","created_at":"2026-05-18T02:27:29.546394+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBE2APQS2XB6","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBE2APQS2XB6L3M6","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBE2APQS","created_at":"2026-05-18T12:27:51.066281+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/MBE2APQS2XB6L3M6EKBK5LS4GP","json":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP.json","graph_json":"https://pith.science/api/pith-number/MBE2APQS2XB6L3M6EKBK5LS4GP/graph.json","events_json":"https://pith.science/api/pith-number/MBE2APQS2XB6L3M6EKBK5LS4GP/events.json","paper":"https://pith.science/paper/MBE2APQS"},"agent_actions":{"view_html":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP","download_json":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP.json","view_paper":"https://pith.science/paper/MBE2APQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0217&json=true","fetch_graph":"https://pith.science/api/pith-number/MBE2APQS2XB6L3M6EKBK5LS4GP/graph.json","fetch_events":"https://pith.science/api/pith-number/MBE2APQS2XB6L3M6EKBK5LS4GP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP/action/storage_attestation","attest_author":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP/action/author_attestation","sign_citation":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP/action/citation_signature","submit_replication":"https://pith.science/pith/MBE2APQS2XB6L3M6EKBK5LS4GP/action/replication_record"}},"created_at":"2026-05-18T02:27:29.546394+00:00","updated_at":"2026-05-18T02:27:29.546394+00:00"}