{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:R33Q3KLRDZFZIV2XUTIQNXL6SY","short_pith_number":"pith:R33Q3KLR","schema_version":"1.0","canonical_sha256":"8ef70da9711e4b945757a4d106dd7e9615aa42291aaceb64dda2e9cf5f956ce9","source":{"kind":"arxiv","id":"1902.00213","version":1},"attestation_state":"computed","paper":{"title":"Comparability and Cocomparability Bigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jephian C.-H. Lin, Jing Huang, Pavol Hell, Ross M. McConnell","submitted_at":"2019-02-01T08:07:59Z","abstract_excerpt":"We propose bipartite analogues of comparability and cocomparability graphs. Surprizingly, the two classes coincide. We call these bipartite graphs cocomparability bigraphs. We characterize cocomparability bigraphs in terms of vertex orderings, forbidden substructures, and orientations of their complements. In particular, we prove that cocomparability bigraphs are precisely those bipartite graphs that do not have edge-asteroids; this is analogous to Gallai's structural characterization of cocomparability graphs by the absence of (vertex-) asteroids. Our characterizations imply a robust polynomi"},"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":"1902.00213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-01T08:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"ec5036b451fabf0460f8219c6c7861625f9e44a5d218824aaf961d5b6fc93185","abstract_canon_sha256":"8e0d75bc85dcb85a3720e6ade0320266ed0f533c89eb6ea598608e2a044e9d0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:58.028285Z","signature_b64":"MQd8gNGgbyAuRZ358pireGMytqtKQHHrdFwcI9BsyXznzRYsQ/EmxAvLfPexcdUuuSrx58uO6bUlb2i7eeB7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ef70da9711e4b945757a4d106dd7e9615aa42291aaceb64dda2e9cf5f956ce9","last_reissued_at":"2026-05-17T23:54:58.027811Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:58.027811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparability and Cocomparability Bigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jephian C.-H. Lin, Jing Huang, Pavol Hell, Ross M. McConnell","submitted_at":"2019-02-01T08:07:59Z","abstract_excerpt":"We propose bipartite analogues of comparability and cocomparability graphs. Surprizingly, the two classes coincide. We call these bipartite graphs cocomparability bigraphs. We characterize cocomparability bigraphs in terms of vertex orderings, forbidden substructures, and orientations of their complements. In particular, we prove that cocomparability bigraphs are precisely those bipartite graphs that do not have edge-asteroids; this is analogous to Gallai's structural characterization of cocomparability graphs by the absence of (vertex-) asteroids. Our characterizations imply a robust polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00213","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":"1902.00213","created_at":"2026-05-17T23:54:58.027880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.00213v1","created_at":"2026-05-17T23:54:58.027880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00213","created_at":"2026-05-17T23:54:58.027880+00:00"},{"alias_kind":"pith_short_12","alias_value":"R33Q3KLRDZFZ","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"R33Q3KLRDZFZIV2X","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"R33Q3KLR","created_at":"2026-05-18T12:33:27.125529+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/R33Q3KLRDZFZIV2XUTIQNXL6SY","json":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY.json","graph_json":"https://pith.science/api/pith-number/R33Q3KLRDZFZIV2XUTIQNXL6SY/graph.json","events_json":"https://pith.science/api/pith-number/R33Q3KLRDZFZIV2XUTIQNXL6SY/events.json","paper":"https://pith.science/paper/R33Q3KLR"},"agent_actions":{"view_html":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY","download_json":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY.json","view_paper":"https://pith.science/paper/R33Q3KLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.00213&json=true","fetch_graph":"https://pith.science/api/pith-number/R33Q3KLRDZFZIV2XUTIQNXL6SY/graph.json","fetch_events":"https://pith.science/api/pith-number/R33Q3KLRDZFZIV2XUTIQNXL6SY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY/action/storage_attestation","attest_author":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY/action/author_attestation","sign_citation":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY/action/citation_signature","submit_replication":"https://pith.science/pith/R33Q3KLRDZFZIV2XUTIQNXL6SY/action/replication_record"}},"created_at":"2026-05-17T23:54:58.027880+00:00","updated_at":"2026-05-17T23:54:58.027880+00:00"}