{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Y5ULAMRGBAASLOF25ORFDBP6S3","short_pith_number":"pith:Y5ULAMRG","schema_version":"1.0","canonical_sha256":"c768b03226080125b8baeba25185fe96faa16c754af97b1086adadfdccfa0f65","source":{"kind":"arxiv","id":"2404.07853","version":1},"attestation_state":"computed","paper":{"title":"Beyond recognizing well-covered graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carl Feghali, Malory Marin, R\\'emi Watrigant","submitted_at":"2024-04-11T15:49:12Z","abstract_excerpt":"We prove a number of results related to the computational complexity of recognizing well-covered graphs. Let $k$ and $s$ be positive integers and let $G$ be a graph. Then $G$ is said\n  - $\\mathbf{W_k}$ if for any $k$ pairwise disjoint independent vertex sets $A_1, \\dots, A_k$ in $G$, there exist $k$ pairwise disjoint maximum independent sets $S_1, \\dots,S_k$ in $G$ such that $A_i \\subseteq S_i$ for $i \\in [k]$.\n  - $\\mathbf{E_s}$ if every independent set in $G$ of size at most $s$ is contained in a maximum independent set in $G$.\n  Chv\\'atal and Slater (1993) and Sankaranarayana and Stewart (1"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2404.07853","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-11T15:49:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"180b481518d61a385ea114565b72f16e35ba2b654cc3312f982357a2fcb2b7f8","abstract_canon_sha256":"440d1ba1fa17f549d7f79538a0387f71d419a8f1664d4f5cdd33dfe8b0a02b17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:58.577877Z","signature_b64":"4BT5mESqj1ZoPwejCqiKjama7W4PZKvLI/v1J2wwbSqstJ3M0gxXBaNhwruGc7ag7K96D0aDJSwIi91SLKO8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c768b03226080125b8baeba25185fe96faa16c754af97b1086adadfdccfa0f65","last_reissued_at":"2026-07-05T08:06:58.577484Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:58.577484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beyond recognizing well-covered graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carl Feghali, Malory Marin, R\\'emi Watrigant","submitted_at":"2024-04-11T15:49:12Z","abstract_excerpt":"We prove a number of results related to the computational complexity of recognizing well-covered graphs. Let $k$ and $s$ be positive integers and let $G$ be a graph. Then $G$ is said\n  - $\\mathbf{W_k}$ if for any $k$ pairwise disjoint independent vertex sets $A_1, \\dots, A_k$ in $G$, there exist $k$ pairwise disjoint maximum independent sets $S_1, \\dots,S_k$ in $G$ such that $A_i \\subseteq S_i$ for $i \\in [k]$.\n  - $\\mathbf{E_s}$ if every independent set in $G$ of size at most $s$ is contained in a maximum independent set in $G$.\n  Chv\\'atal and Slater (1993) and Sankaranarayana and Stewart (1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07853","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.07853/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.07853","created_at":"2026-07-05T08:06:58.577540+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.07853v1","created_at":"2026-07-05T08:06:58.577540+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07853","created_at":"2026-07-05T08:06:58.577540+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y5ULAMRGBAAS","created_at":"2026-07-05T08:06:58.577540+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y5ULAMRGBAASLOF2","created_at":"2026-07-05T08:06:58.577540+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y5ULAMRG","created_at":"2026-07-05T08:06:58.577540+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3","json":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3.json","graph_json":"https://pith.science/api/pith-number/Y5ULAMRGBAASLOF25ORFDBP6S3/graph.json","events_json":"https://pith.science/api/pith-number/Y5ULAMRGBAASLOF25ORFDBP6S3/events.json","paper":"https://pith.science/paper/Y5ULAMRG"},"agent_actions":{"view_html":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3","download_json":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3.json","view_paper":"https://pith.science/paper/Y5ULAMRG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.07853&json=true","fetch_graph":"https://pith.science/api/pith-number/Y5ULAMRGBAASLOF25ORFDBP6S3/graph.json","fetch_events":"https://pith.science/api/pith-number/Y5ULAMRGBAASLOF25ORFDBP6S3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3/action/storage_attestation","attest_author":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3/action/author_attestation","sign_citation":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3/action/citation_signature","submit_replication":"https://pith.science/pith/Y5ULAMRGBAASLOF25ORFDBP6S3/action/replication_record"}},"created_at":"2026-07-05T08:06:58.577540+00:00","updated_at":"2026-07-05T08:06:58.577540+00:00"}