{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V6CEM5GD5PRVQN2DBPCGDKPA5B","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":"fb422353f0588d6ba5d9272720063327d4104f91e173fdbb11858851b579cdd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-12T20:38:01Z","title_canon_sha256":"fbd828d79ea2ba2ce4b027e6c409069e724218ce25da45e2a9a76e93dea4bd83"},"schema_version":"1.0","source":{"id":"1508.03062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03062","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03062v2","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03062","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"V6CEM5GD5PRV","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V6CEM5GD5PRVQN2D","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V6CEM5GD","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:2f837a7bc8ba7729b8a572a7322a7ecb4a73b8c10c57ea50fd3fa47b6f3ed937","target":"graph","created_at":"2026-05-18T00:49:52Z","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 hole is a chordless cycle with at least four vertices. A pan is a graph which consists of a hole and a single vertex with precisely one neighbor on the hole. An even hole is a hole with an even number of vertices. We prove that a (pan, even hole)-free graph can be decomposed by clique cutsets into essentially unit circular-arc graphs. This structure theorem is the basis of our $O(nm)$-time certifying algorithm for recognizing (pan, even hole)-free graphs and for our $O(n^{2.5}+nm)$-time algorithm to optimally color them. Using this structure theorem, we show that the tree-width of a (pan, ev","authors_text":"Chinh T. Hoang, Kathie Cameron, Steven Chaplick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-12T20:38:01Z","title":"On the structure of (pan, even hole)-free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03062","kind":"arxiv","version":2},"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":"sha256:43057406faa696fc684e1fe6982cb4b16af1645d63696c73dab42d6c85ace69a","target":"record","created_at":"2026-05-18T00:49:52Z","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":"fb422353f0588d6ba5d9272720063327d4104f91e173fdbb11858851b579cdd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-12T20:38:01Z","title_canon_sha256":"fbd828d79ea2ba2ce4b027e6c409069e724218ce25da45e2a9a76e93dea4bd83"},"schema_version":"1.0","source":{"id":"1508.03062","kind":"arxiv","version":2}},"canonical_sha256":"af844674c3ebe35837430bc461a9e0e86e6aef5cc5aee9203fa2b7bbf18cfcf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af844674c3ebe35837430bc461a9e0e86e6aef5cc5aee9203fa2b7bbf18cfcf7","first_computed_at":"2026-05-18T00:49:52.624155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:52.624155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wOxL4NeL0H8LPj4z5LzM4TpGWp50Ey/uyi1ZJyZqoPjoPUz2FvArLpe8pQkE8w8N3rwzD6CPf0CqA10R0Q0EBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:52.624656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43057406faa696fc684e1fe6982cb4b16af1645d63696c73dab42d6c85ace69a","sha256:2f837a7bc8ba7729b8a572a7322a7ecb4a73b8c10c57ea50fd3fa47b6f3ed937"],"state_sha256":"e4b087b5a79d35ca8192d6556dd50c3a1a3f734ad5d2ae11cba254b47cd8c41f"}