{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LZWAQDEMSJLKWD7DK5DVOOIBBH","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":"55ca6ad3c26c5fb8f6801e942274d3ab0026ab23b5e8fb400636a7282709051f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-28T04:50:49Z","title_canon_sha256":"5e24cfa3fc7a659c5d33ab7169b9a9aa7caf2fd7d09dbd28139f3604cf87e066"},"schema_version":"1.0","source":{"id":"1808.09117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09117","created_at":"2026-05-18T00:07:04Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09117v1","created_at":"2026-05-18T00:07:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09117","created_at":"2026-05-18T00:07:04Z"},{"alias_kind":"pith_short_12","alias_value":"LZWAQDEMSJLK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LZWAQDEMSJLKWD7D","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LZWAQDEM","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:c08afd51c51edae939d79a031cb6cd5b0f90eeb56544f25f143dcd3bd723f6b5","target":"graph","created_at":"2026-05-18T00:07:04Z","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":"The family of graphs that can be constructed from isolated vertices by disjoint union and graph join operations are called cographs. These graphs can be represented in a tree-like representation termed parse tree or cotree. In this paper, we study some popular combinatorial problems restricted to cographs. We first present a structural characterization of minimal vertex separators in cographs. Further, we show that listing all minimal vertex separators and the complexity of some constrained vertex separators are polynomial-time solvable in cographs. We propose polynomial-time algorithms for co","authors_text":"Kona Harshita, N. Sadagopan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-28T04:50:49Z","title":"On Some Combinatorial Problems in Cographs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09117","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":"sha256:292b9d3f560346efdf3a8904537117f8b556ea573c088a28846ff440a0144a17","target":"record","created_at":"2026-05-18T00:07:04Z","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":"55ca6ad3c26c5fb8f6801e942274d3ab0026ab23b5e8fb400636a7282709051f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-28T04:50:49Z","title_canon_sha256":"5e24cfa3fc7a659c5d33ab7169b9a9aa7caf2fd7d09dbd28139f3604cf87e066"},"schema_version":"1.0","source":{"id":"1808.09117","kind":"arxiv","version":1}},"canonical_sha256":"5e6c080c8c9256ab0fe3574757390109f31f46092e0199c70f985c7139447927","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e6c080c8c9256ab0fe3574757390109f31f46092e0199c70f985c7139447927","first_computed_at":"2026-05-18T00:07:04.440783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:04.440783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j/1UEzajjoV4q90HbwGJoIUwVybfUhYdsDUcLfn2w3ZQXJgvm6a1SlzXeID+GiZ1GB8cYVwsX0ylzEvG2Po2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:04.441360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:292b9d3f560346efdf3a8904537117f8b556ea573c088a28846ff440a0144a17","sha256:c08afd51c51edae939d79a031cb6cd5b0f90eeb56544f25f143dcd3bd723f6b5"],"state_sha256":"9a847513d89146bced36203f9e4cdd3a16468651da5f0e3c6e9a3d4ee8833b24"}