{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XERZER2ZGMBSKS4MEKCJFLUVX6","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":"d2d7f6b199b4dbb418c12d628c8ffef331130716a36de5ca864cfd7ab00980d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-14T08:54:32Z","title_canon_sha256":"c37d1ac14c20e6a271c4d4188c84a7c91bab96e7c142cd5f81b9c447c68b176d"},"schema_version":"1.0","source":{"id":"1105.2874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2874","created_at":"2026-05-18T04:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2874v1","created_at":"2026-05-18T04:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2874","created_at":"2026-05-18T04:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"XERZER2ZGMBS","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XERZER2ZGMBSKS4M","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XERZER2Z","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:155940d55cde107135ab83b853a38cc4d3deb7e5c54b8c97c0860bfc28a47622","target":"graph","created_at":"2026-05-18T04:22:01Z","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":"Clique separator decomposition introduced by Tarjan and Whitesides is one of the most important graph decompositions. A graph is an {\\em atom} if it has no clique separator. A {\\em hole} is a chordless cycle with at least five vertices, and an {\\em antihole} is the complement graph of a hole. A graph is {\\em weakly chordal} if it is hole- and antihole-free. $K_4-e$ is also called {\\em diamond}. {\\em Paraglider} has five vertices four of which induce a diamond, and the fifth vertex sees exactly the two vertices of degree two in the diamond. In this paper we show that atoms of hole- and diamond-","authors_text":"Andreas Brandst\\\"adt, Vassilis Giakoumakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-14T08:54:32Z","title":"Clique Separator Decomposition of Hole- and Diamond-Free Graphs and Algorithmic Consequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2874","kind":"arxiv","version":1},"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":"sha256:5ca75f2e82437178b3f38a8c07e3086bebd17e2a386f2d2933df8b02c941bb77","target":"record","created_at":"2026-05-18T04:22:01Z","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":"d2d7f6b199b4dbb418c12d628c8ffef331130716a36de5ca864cfd7ab00980d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-14T08:54:32Z","title_canon_sha256":"c37d1ac14c20e6a271c4d4188c84a7c91bab96e7c142cd5f81b9c447c68b176d"},"schema_version":"1.0","source":{"id":"1105.2874","kind":"arxiv","version":1}},"canonical_sha256":"b9239247593303254b8c228492ae95bfbedfe2ef8e3fac7087315f431bd0c8a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9239247593303254b8c228492ae95bfbedfe2ef8e3fac7087315f431bd0c8a4","first_computed_at":"2026-05-18T04:22:01.845395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:01.845395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbjj2eLyGOm1HMwsFB6AyscPYFoDnG0pG8wLu0K5c3ttlRrwPtz8yNXnbVWIqlfOkpBuuqGBZtYmATZ2booXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:01.845898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ca75f2e82437178b3f38a8c07e3086bebd17e2a386f2d2933df8b02c941bb77","sha256:155940d55cde107135ab83b853a38cc4d3deb7e5c54b8c97c0860bfc28a47622"],"state_sha256":"e3933ba2ef627b166597123f7a34448083dd432cf29ff7be780dd53869ded402"}