{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OZA2NZAE3WKLOLD67GJ33VJPT3","short_pith_number":"pith:OZA2NZAE","schema_version":"1.0","canonical_sha256":"7641a6e404dd94b72c7ef993bdd52f9ec225603f5a5271b9992265e1305af224","source":{"kind":"arxiv","id":"1201.5707","version":2},"attestation_state":"computed","paper":{"title":"Hamiltonicity of 3-arc graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangjun Xu, Sanming Zhou","submitted_at":"2012-01-27T06:27:56Z","abstract_excerpt":"An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-"},"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":"1201.5707","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-27T06:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"7b7eff696f64f1688f4c25655fc0272786646b9c3680ca47da1e609d3362ad56","abstract_canon_sha256":"f407b834949843040192c3cd7063573608bb94936c0042ce387c4a2eb90f053a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:21.066248Z","signature_b64":"qCcIqXv8+okrezpkZYppQlQrPQrV7kCHA4PBGokX4tVlDXVBRojJXugRrwSS78v2x+vQq0FlUiNRmsbshAXuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7641a6e404dd94b72c7ef993bdd52f9ec225603f5a5271b9992265e1305af224","last_reissued_at":"2026-05-18T03:07:21.065796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:21.065796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonicity of 3-arc graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangjun Xu, Sanming Zhou","submitted_at":"2012-01-27T06:27:56Z","abstract_excerpt":"An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5707","kind":"arxiv","version":2},"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":"1201.5707","created_at":"2026-05-18T03:07:21.065860+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5707v2","created_at":"2026-05-18T03:07:21.065860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5707","created_at":"2026-05-18T03:07:21.065860+00:00"},{"alias_kind":"pith_short_12","alias_value":"OZA2NZAE3WKL","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"OZA2NZAE3WKLOLD6","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"OZA2NZAE","created_at":"2026-05-18T12:27:18.751474+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/OZA2NZAE3WKLOLD67GJ33VJPT3","json":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3.json","graph_json":"https://pith.science/api/pith-number/OZA2NZAE3WKLOLD67GJ33VJPT3/graph.json","events_json":"https://pith.science/api/pith-number/OZA2NZAE3WKLOLD67GJ33VJPT3/events.json","paper":"https://pith.science/paper/OZA2NZAE"},"agent_actions":{"view_html":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3","download_json":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3.json","view_paper":"https://pith.science/paper/OZA2NZAE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5707&json=true","fetch_graph":"https://pith.science/api/pith-number/OZA2NZAE3WKLOLD67GJ33VJPT3/graph.json","fetch_events":"https://pith.science/api/pith-number/OZA2NZAE3WKLOLD67GJ33VJPT3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3/action/storage_attestation","attest_author":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3/action/author_attestation","sign_citation":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3/action/citation_signature","submit_replication":"https://pith.science/pith/OZA2NZAE3WKLOLD67GJ33VJPT3/action/replication_record"}},"created_at":"2026-05-18T03:07:21.065860+00:00","updated_at":"2026-05-18T03:07:21.065860+00:00"}