{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SQSNAVDTPE375CNNIP4X76ZQ5Z","short_pith_number":"pith:SQSNAVDT","schema_version":"1.0","canonical_sha256":"9424d054737937fe89ad43f97ffb30ee5d17ee74f8e5d1224cc3238c29796e10","source":{"kind":"arxiv","id":"1511.02038","version":2},"attestation_state":"computed","paper":{"title":"2-Trees: Structural Insights and the study of Hamiltonian Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"N. Sadagopan, P. Renjith","submitted_at":"2015-11-06T11:39:15Z","abstract_excerpt":"For a connected graph, a path containing all vertices is known as \\emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a Hamiltonian path in general graphs is NP-Complete. We present a necessary and sufficient condition for the existence of Hamiltonian paths in 2-trees. Using our characterization, we also present a linear-time algorithm for the existence of Hamiltonian paths in 2-trees. Our characterization is based on a deep understanding of the structure of 2-trees and the combin"},"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":"1511.02038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-11-06T11:39:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"80a7208bb2736be218c735be14f294b9ff779fd36bcfc8013f3b7c1820bd0577","abstract_canon_sha256":"03e86ecc6347b2ab6419c2404113256f37a3544df96a71e2bf6f05d086b4a6fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:45.832580Z","signature_b64":"yBzUgFhZ10+n1N4C5Y9phf+t4/K0cYEAqbskcsU0Afa6PCzVxLGscRzrS1V3RO9nCOuOq8t6VhCE/45TGcSfBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9424d054737937fe89ad43f97ffb30ee5d17ee74f8e5d1224cc3238c29796e10","last_reissued_at":"2026-05-18T01:10:45.832204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:45.832204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2-Trees: Structural Insights and the study of Hamiltonian Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"N. Sadagopan, P. Renjith","submitted_at":"2015-11-06T11:39:15Z","abstract_excerpt":"For a connected graph, a path containing all vertices is known as \\emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a Hamiltonian path in general graphs is NP-Complete. We present a necessary and sufficient condition for the existence of Hamiltonian paths in 2-trees. Using our characterization, we also present a linear-time algorithm for the existence of Hamiltonian paths in 2-trees. Our characterization is based on a deep understanding of the structure of 2-trees and the combin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02038","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":"1511.02038","created_at":"2026-05-18T01:10:45.832261+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02038v2","created_at":"2026-05-18T01:10:45.832261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02038","created_at":"2026-05-18T01:10:45.832261+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQSNAVDTPE37","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQSNAVDTPE375CNN","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQSNAVDT","created_at":"2026-05-18T12:29:42.218222+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/SQSNAVDTPE375CNNIP4X76ZQ5Z","json":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z.json","graph_json":"https://pith.science/api/pith-number/SQSNAVDTPE375CNNIP4X76ZQ5Z/graph.json","events_json":"https://pith.science/api/pith-number/SQSNAVDTPE375CNNIP4X76ZQ5Z/events.json","paper":"https://pith.science/paper/SQSNAVDT"},"agent_actions":{"view_html":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z","download_json":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z.json","view_paper":"https://pith.science/paper/SQSNAVDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02038&json=true","fetch_graph":"https://pith.science/api/pith-number/SQSNAVDTPE375CNNIP4X76ZQ5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/SQSNAVDTPE375CNNIP4X76ZQ5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z/action/storage_attestation","attest_author":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z/action/author_attestation","sign_citation":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z/action/citation_signature","submit_replication":"https://pith.science/pith/SQSNAVDTPE375CNNIP4X76ZQ5Z/action/replication_record"}},"created_at":"2026-05-18T01:10:45.832261+00:00","updated_at":"2026-05-18T01:10:45.832261+00:00"}