{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UWLPFPP4WDXCSEGKWN3EZIZZCW","short_pith_number":"pith:UWLPFPP4","schema_version":"1.0","canonical_sha256":"a596f2bdfcb0ee2910cab3764ca33915804a857221525d0a5157a92ad1b95020","source":{"kind":"arxiv","id":"1609.01367","version":1},"attestation_state":"computed","paper":{"title":"When Two-Holed Torus Graphs are Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dhruv Rohatgi","submitted_at":"2016-09-06T01:45:16Z","abstract_excerpt":"Trotter and Erd\\\"os found conditions for when a directed $m \\times n$ grid graph on a torus is Hamiltonian. We consider the analogous graphs on a two-holed torus, and study their Hamiltonicity. We find an $\\mathcal{O}(n^4)$ algorithm to determine the Hamiltonicity of one of these graphs and an $\\mathcal{O}(\\log(n))$ algorithm to find the number of diagonals, which are sets of vertices that force the directions of edges in any Hamiltonian cycle. We also show that there is a periodicity pattern in the graphs' Hamiltonicities if one of the sides of the grid is fixed; and we completely classify wh"},"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":"1609.01367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T01:45:16Z","cross_cats_sorted":[],"title_canon_sha256":"2ef0808c4fa46ba725e079c7051466f4ae8e0e6df755a0f4f3b7b395300d6633","abstract_canon_sha256":"3ad893ef4b88bec73c7fa642200d9e89a162714383161506a749b0edc672736a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:39.765392Z","signature_b64":"Sg/kYowY4TH3NeUkBZubYBSNBAVZ0deEHQ2SW38JXAS/zfFybRb8Av7pRXaLRUYMPVahToYAvfUKNx8dCk0lCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a596f2bdfcb0ee2910cab3764ca33915804a857221525d0a5157a92ad1b95020","last_reissued_at":"2026-05-18T01:05:39.764911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:39.764911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When Two-Holed Torus Graphs are Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dhruv Rohatgi","submitted_at":"2016-09-06T01:45:16Z","abstract_excerpt":"Trotter and Erd\\\"os found conditions for when a directed $m \\times n$ grid graph on a torus is Hamiltonian. We consider the analogous graphs on a two-holed torus, and study their Hamiltonicity. We find an $\\mathcal{O}(n^4)$ algorithm to determine the Hamiltonicity of one of these graphs and an $\\mathcal{O}(\\log(n))$ algorithm to find the number of diagonals, which are sets of vertices that force the directions of edges in any Hamiltonian cycle. We also show that there is a periodicity pattern in the graphs' Hamiltonicities if one of the sides of the grid is fixed; and we completely classify wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01367","kind":"arxiv","version":1},"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":"1609.01367","created_at":"2026-05-18T01:05:39.764993+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01367v1","created_at":"2026-05-18T01:05:39.764993+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01367","created_at":"2026-05-18T01:05:39.764993+00:00"},{"alias_kind":"pith_short_12","alias_value":"UWLPFPP4WDXC","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UWLPFPP4WDXCSEGK","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UWLPFPP4","created_at":"2026-05-18T12:30:46.583412+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/UWLPFPP4WDXCSEGKWN3EZIZZCW","json":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW.json","graph_json":"https://pith.science/api/pith-number/UWLPFPP4WDXCSEGKWN3EZIZZCW/graph.json","events_json":"https://pith.science/api/pith-number/UWLPFPP4WDXCSEGKWN3EZIZZCW/events.json","paper":"https://pith.science/paper/UWLPFPP4"},"agent_actions":{"view_html":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW","download_json":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW.json","view_paper":"https://pith.science/paper/UWLPFPP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01367&json=true","fetch_graph":"https://pith.science/api/pith-number/UWLPFPP4WDXCSEGKWN3EZIZZCW/graph.json","fetch_events":"https://pith.science/api/pith-number/UWLPFPP4WDXCSEGKWN3EZIZZCW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW/action/storage_attestation","attest_author":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW/action/author_attestation","sign_citation":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW/action/citation_signature","submit_replication":"https://pith.science/pith/UWLPFPP4WDXCSEGKWN3EZIZZCW/action/replication_record"}},"created_at":"2026-05-18T01:05:39.764993+00:00","updated_at":"2026-05-18T01:05:39.764993+00:00"}