{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DSU3XORZV3NKGLC67VYURNJNO5","short_pith_number":"pith:DSU3XORZ","schema_version":"1.0","canonical_sha256":"1ca9bbba39aedaa32c5efd7148b52d776bc9009ef1a92d6823ef555d93371808","source":{"kind":"arxiv","id":"1206.0233","version":3},"attestation_state":"computed","paper":{"title":"3-Colourability of Dually Chordal Graphs in Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Arne Leitert","submitted_at":"2012-06-01T16:00:59Z","abstract_excerpt":"A graph G is dually chordal if there is a spanning tree T of G such that any maximal clique of G induces a subtree in T. This paper investigates the Colourability problem on dually chordal graphs. It will show that it is NP-complete in case of four colours and solvable in linear time with a simple algorithm in case of three colours. In addition, it will be shown that a dually chordal graph is 3-colourable if and only if it is perfect and has no clique of size four."},"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":"1206.0233","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-06-01T16:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"9d4a85a01651a9a2e1c8a5098509a0c0412e7ab3c6ed1a2cdab84e0e440fcc9e","abstract_canon_sha256":"ae8b78c18055a10ab629939bc22feed04b7029d72e43288091d3909d5ece01b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:01.089736Z","signature_b64":"Zq5iCyIuqylP0XV9VzhAHgBjJ/OLI14ue4+499qhMkQbMS9XB3MFWVo1kVyIIhqOFE3uNIy4yBCsRaprLyk8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ca9bbba39aedaa32c5efd7148b52d776bc9009ef1a92d6823ef555d93371808","last_reissued_at":"2026-05-18T03:41:01.089056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:01.089056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"3-Colourability of Dually Chordal Graphs in Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Arne Leitert","submitted_at":"2012-06-01T16:00:59Z","abstract_excerpt":"A graph G is dually chordal if there is a spanning tree T of G such that any maximal clique of G induces a subtree in T. This paper investigates the Colourability problem on dually chordal graphs. It will show that it is NP-complete in case of four colours and solvable in linear time with a simple algorithm in case of three colours. In addition, it will be shown that a dually chordal graph is 3-colourable if and only if it is perfect and has no clique of size four."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0233","kind":"arxiv","version":3},"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":"1206.0233","created_at":"2026-05-18T03:41:01.089164+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.0233v3","created_at":"2026-05-18T03:41:01.089164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0233","created_at":"2026-05-18T03:41:01.089164+00:00"},{"alias_kind":"pith_short_12","alias_value":"DSU3XORZV3NK","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DSU3XORZV3NKGLC6","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DSU3XORZ","created_at":"2026-05-18T12:27:04.183437+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/DSU3XORZV3NKGLC67VYURNJNO5","json":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5.json","graph_json":"https://pith.science/api/pith-number/DSU3XORZV3NKGLC67VYURNJNO5/graph.json","events_json":"https://pith.science/api/pith-number/DSU3XORZV3NKGLC67VYURNJNO5/events.json","paper":"https://pith.science/paper/DSU3XORZ"},"agent_actions":{"view_html":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5","download_json":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5.json","view_paper":"https://pith.science/paper/DSU3XORZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.0233&json=true","fetch_graph":"https://pith.science/api/pith-number/DSU3XORZV3NKGLC67VYURNJNO5/graph.json","fetch_events":"https://pith.science/api/pith-number/DSU3XORZV3NKGLC67VYURNJNO5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5/action/storage_attestation","attest_author":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5/action/author_attestation","sign_citation":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5/action/citation_signature","submit_replication":"https://pith.science/pith/DSU3XORZV3NKGLC67VYURNJNO5/action/replication_record"}},"created_at":"2026-05-18T03:41:01.089164+00:00","updated_at":"2026-05-18T03:41:01.089164+00:00"}