{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DSU3XORZV3NKGLC67VYURNJNO5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ae8b78c18055a10ab629939bc22feed04b7029d72e43288091d3909d5ece01b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-06-01T16:00:59Z","title_canon_sha256":"9d4a85a01651a9a2e1c8a5098509a0c0412e7ab3c6ed1a2cdab84e0e440fcc9e"},"schema_version":"1.0","source":{"id":"1206.0233","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0233","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0233v3","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0233","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"DSU3XORZV3NK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DSU3XORZV3NKGLC6","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DSU3XORZ","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:83dd74fe4366add9ba76a36d47748d041d92a8d0c8409bb3ec581f9af7f0079b","target":"graph","created_at":"2026-05-18T03:41:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Arne Leitert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-06-01T16:00:59Z","title":"3-Colourability of Dually Chordal Graphs in Linear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0233","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c7ca5ae36afe967d2b3c2ab8843fab3f24cb4cbf1e9747971c23dc0db7ef6409","target":"record","created_at":"2026-05-18T03:41:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae8b78c18055a10ab629939bc22feed04b7029d72e43288091d3909d5ece01b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-06-01T16:00:59Z","title_canon_sha256":"9d4a85a01651a9a2e1c8a5098509a0c0412e7ab3c6ed1a2cdab84e0e440fcc9e"},"schema_version":"1.0","source":{"id":"1206.0233","kind":"arxiv","version":3}},"canonical_sha256":"1ca9bbba39aedaa32c5efd7148b52d776bc9009ef1a92d6823ef555d93371808","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca9bbba39aedaa32c5efd7148b52d776bc9009ef1a92d6823ef555d93371808","first_computed_at":"2026-05-18T03:41:01.089056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:01.089056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zq5iCyIuqylP0XV9VzhAHgBjJ/OLI14ue4+499qhMkQbMS9XB3MFWVo1kVyIIhqOFE3uNIy4yBCsRaprLyk8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:01.089736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0233","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7ca5ae36afe967d2b3c2ab8843fab3f24cb4cbf1e9747971c23dc0db7ef6409","sha256:83dd74fe4366add9ba76a36d47748d041d92a8d0c8409bb3ec581f9af7f0079b"],"state_sha256":"fc2a1787ec12fe789a5cafe91283c7804aa8e7a592446a17258eba602f43c328"}