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Abreu et al. conjectured that $K_{3,3}$, the Heawood graph and the Pappus graph are the only essentially 4-edge-connected pseudo 2-factor isomorphic cubic bipartite graphs (Abreu et al., Journal of Combinatorial Theory, Series B, 2008, Conjecture 3.6).\n  Using a computer search we show that this conjecture is false by constructing a counterexample with 30 vertices. We also show that this is the only counterexample up to at least 40 vertices.\n  A graph $G$ is 2-fac"},"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":"1412.3350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-10T16:00:47Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"93bbd69184b8f32cd72d1ed07113aa868b49d1c7cc9fe0a4fdb1c49b6d631de0","abstract_canon_sha256":"8550bebab46d7861ed99517c547371e1118cf859fec1146f454f7140ae153b94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:08.091690Z","signature_b64":"CxEwVxXrGKNDP/tR7ozoGGPpRjhRoYoFSxnwPKbk/CXC52w76VOGecOJ4i8Dwnl3xKd8oTfRuQQuqBhyshibCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c4019c16dc58b5447281d0e4974bb80c6713b0de01cbd0adeca618068498f85","last_reissued_at":"2026-05-18T02:02:08.091064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:08.091064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A counterexample to the pseudo 2-factor isomorphic graph conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Goedgebeur","submitted_at":"2014-12-10T16:00:47Z","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 $G$. Abreu et al. conjectured that $K_{3,3}$, the Heawood graph and the Pappus graph are the only essentially 4-edge-connected pseudo 2-factor isomorphic cubic bipartite graphs (Abreu et al., Journal of Combinatorial Theory, Series B, 2008, Conjecture 3.6).\n  Using a computer search we show that this conjecture is false by constructing a counterexample with 30 vertices. We also show that this is the only counterexample up to at least 40 vertices.\n  A graph $G$ is 2-fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3350","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":"1412.3350","created_at":"2026-05-18T02:02:08.091140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.3350v2","created_at":"2026-05-18T02:02:08.091140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3350","created_at":"2026-05-18T02:02:08.091140+00:00"},{"alias_kind":"pith_short_12","alias_value":"JRABTQLNYWFV","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JRABTQLNYWFVIRZI","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JRABTQLN","created_at":"2026-05-18T12:28:35.611951+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/JRABTQLNYWFVIRZIDUHES5F3QD","json":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD.json","graph_json":"https://pith.science/api/pith-number/JRABTQLNYWFVIRZIDUHES5F3QD/graph.json","events_json":"https://pith.science/api/pith-number/JRABTQLNYWFVIRZIDUHES5F3QD/events.json","paper":"https://pith.science/paper/JRABTQLN"},"agent_actions":{"view_html":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD","download_json":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD.json","view_paper":"https://pith.science/paper/JRABTQLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.3350&json=true","fetch_graph":"https://pith.science/api/pith-number/JRABTQLNYWFVIRZIDUHES5F3QD/graph.json","fetch_events":"https://pith.science/api/pith-number/JRABTQLNYWFVIRZIDUHES5F3QD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD/action/storage_attestation","attest_author":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD/action/author_attestation","sign_citation":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD/action/citation_signature","submit_replication":"https://pith.science/pith/JRABTQLNYWFVIRZIDUHES5F3QD/action/replication_record"}},"created_at":"2026-05-18T02:02:08.091140+00:00","updated_at":"2026-05-18T02:02:08.091140+00:00"}