{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OTI2QWBH3OA6RH6FRF5VY74MS6","short_pith_number":"pith:OTI2QWBH","schema_version":"1.0","canonical_sha256":"74d1a85827db81e89fc5897b5c7f8c9786fec0d4dac97a225e7e1253e8148a32","source":{"kind":"arxiv","id":"1002.1033","version":1},"attestation_state":"computed","paper":{"title":"Pseudo and Strongly Pseudo 2--Factor Isomorphic Regular Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Labbate, J. Sheehan, M. Abreu","submitted_at":"2010-02-04T16:26:48Z","abstract_excerpt":"A graph $G$ is pseudo 2--factor isomorphic if the parity of the number of cycles in a 2--factor is the same for all 2--factors of $G$. In \\cite{ADJLS} we proved that pseudo 2--factor isomorphic $k$--regular bipartite graphs exist only for $k \\le 3$. In this paper we generalize this result for regular graphs which are not necessarily bipartite. We also introduce strongly pseudo 2--factor isomorphic graphs and we prove that pseudo and strongly pseudo 2--factor isomorphic 2k--regular graphs and $k$--regular digraphs do not exist for $k\\geq 4$. Moreover, we present constructions of infinite famili"},"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":"1002.1033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-02-04T16:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"e11f878506d33839dce4cebff8660e1e8cc4d9e095196dfb1ac7607a6ede666f","abstract_canon_sha256":"65ea528bdedf0c3fecb09305f1aeeb09890e36521dc328f2197fb5e4a02d2844"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:44.479752Z","signature_b64":"FiFkBBImzGUUE87+u0X4hta8e3ORbV+3WITrvUl5d5KgqjVPzKtsfEEAOmVl3JCgV95wwWItmWieAQD+0WfvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74d1a85827db81e89fc5897b5c7f8c9786fec0d4dac97a225e7e1253e8148a32","last_reissued_at":"2026-05-18T02:29:44.479293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:44.479293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo and Strongly Pseudo 2--Factor Isomorphic Regular Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Labbate, J. Sheehan, M. Abreu","submitted_at":"2010-02-04T16:26:48Z","abstract_excerpt":"A graph $G$ is pseudo 2--factor isomorphic if the parity of the number of cycles in a 2--factor is the same for all 2--factors of $G$. In \\cite{ADJLS} we proved that pseudo 2--factor isomorphic $k$--regular bipartite graphs exist only for $k \\le 3$. In this paper we generalize this result for regular graphs which are not necessarily bipartite. We also introduce strongly pseudo 2--factor isomorphic graphs and we prove that pseudo and strongly pseudo 2--factor isomorphic 2k--regular graphs and $k$--regular digraphs do not exist for $k\\geq 4$. Moreover, we present constructions of infinite famili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1033","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":"1002.1033","created_at":"2026-05-18T02:29:44.479404+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.1033v1","created_at":"2026-05-18T02:29:44.479404+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1033","created_at":"2026-05-18T02:29:44.479404+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTI2QWBH3OA6","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTI2QWBH3OA6RH6F","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTI2QWBH","created_at":"2026-05-18T12:26:12.377268+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/OTI2QWBH3OA6RH6FRF5VY74MS6","json":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6.json","graph_json":"https://pith.science/api/pith-number/OTI2QWBH3OA6RH6FRF5VY74MS6/graph.json","events_json":"https://pith.science/api/pith-number/OTI2QWBH3OA6RH6FRF5VY74MS6/events.json","paper":"https://pith.science/paper/OTI2QWBH"},"agent_actions":{"view_html":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6","download_json":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6.json","view_paper":"https://pith.science/paper/OTI2QWBH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.1033&json=true","fetch_graph":"https://pith.science/api/pith-number/OTI2QWBH3OA6RH6FRF5VY74MS6/graph.json","fetch_events":"https://pith.science/api/pith-number/OTI2QWBH3OA6RH6FRF5VY74MS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6/action/storage_attestation","attest_author":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6/action/author_attestation","sign_citation":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6/action/citation_signature","submit_replication":"https://pith.science/pith/OTI2QWBH3OA6RH6FRF5VY74MS6/action/replication_record"}},"created_at":"2026-05-18T02:29:44.479404+00:00","updated_at":"2026-05-18T02:29:44.479404+00:00"}