{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:B47MMXAS4SX6CKEJYPNSTJ43AD","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":"00fbd5bf237761bbff0cf1e3b138443ab31255e0f02817ab000d986a71464c5d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-03T15:01:07Z","title_canon_sha256":"86f52e3d4277fd877bf77f4ef8bde8b9f6ad467f39f673297c1498b44bbd2389"},"schema_version":"1.0","source":{"id":"1111.0867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0867","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0867v1","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0867","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"B47MMXAS4SX6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B47MMXAS4SX6CKEJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B47MMXAS","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:f8eba973786169c444bb466e21cfa4094ad0823520964c69892bd3599d70de25","target":"graph","created_at":"2026-05-18T04:09:36Z","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":"Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B|=b and |W|=w such that no vertex in B is adjacent to any vertex in W. In this paper we show that the problem is polynomial when restricted to cographs, distance-hereditary graphs, interval graphs and strongly chordal graphs. We show that the problem is NP-complete on splitgraphs.","authors_text":"Feng-Ren Tsai, Sheung-Hung Poon, Ton Kloks, Yue-Li Wang","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-03T15:01:07Z","title":"The black-and-white coloring problem on distance hereditary graphs and strongly chordal graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0867","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:ad81f80c9dadf4c57e0df22e16fd1ede14faf6d66ac52a0fe1e6d18f9e7fc008","target":"record","created_at":"2026-05-18T04:09:36Z","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":"00fbd5bf237761bbff0cf1e3b138443ab31255e0f02817ab000d986a71464c5d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-03T15:01:07Z","title_canon_sha256":"86f52e3d4277fd877bf77f4ef8bde8b9f6ad467f39f673297c1498b44bbd2389"},"schema_version":"1.0","source":{"id":"1111.0867","kind":"arxiv","version":1}},"canonical_sha256":"0f3ec65c12e4afe12889c3db29a79b00df09870f935f159c87cc52fb267ed595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f3ec65c12e4afe12889c3db29a79b00df09870f935f159c87cc52fb267ed595","first_computed_at":"2026-05-18T04:09:36.080864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:36.080864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OQ+mwFfKrErlLHccfmDY8EiBwKspzgBUUkALpsA5Hf73JaVGb7FXzk/dtotjwZ3IufXO3LYV+SlAcNk0MlNgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:36.081391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad81f80c9dadf4c57e0df22e16fd1ede14faf6d66ac52a0fe1e6d18f9e7fc008","sha256:f8eba973786169c444bb466e21cfa4094ad0823520964c69892bd3599d70de25"],"state_sha256":"72922ea2038230837817412650db4ce1c6b3f75d9f635fe0b3b573405efced07"}