{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:2XYANUXTZTMFIVQCJFFCNNZKWM","short_pith_number":"pith:2XYANUXT","schema_version":"1.0","canonical_sha256":"d5f006d2f3ccd8545602494a26b72ab31c7719c47eb02ceb4fb99264f211e8c1","source":{"kind":"arxiv","id":"0906.4609","version":2},"attestation_state":"computed","paper":{"title":"Critical independent sets and Konig--Egervary graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Eugen Mandrescu, Vadim E. Levit","submitted_at":"2009-06-25T15:09:41Z","abstract_excerpt":"Let alpha(G) be the cardinality of a independence set of maximum size in the graph G, while mu(G) is the size of a maximum matching. G is a Konig--Egervary graph if its order equals alpha(G) + mu(G). The set core(G) is the intersection of all maximum independent sets of G (Levit & Mandrescu, 2002). The number def(G)=|V(G)|-2*mu(G) is the deficiency of G (Lovasz & Plummer, 1986). The number d(G)=max{|S|-|N(S)|:S in Ind(G)} is the critical difference of G. An independent set A is critical if |A|-|N(A)|=d(G), where N(S) is the neighborhood of S (Zhang, 1990). In 2009, Larson showed that G is Koni"},"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":"0906.4609","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-06-25T15:09:41Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"abe7215d5e787d23c00c46f8d1fbd216892419f2fdb7449ea0974cd2d9028881","abstract_canon_sha256":"7664a38ecc626bb49bc1e6eb06d557e3903590720f0eedda2d94c1a25fdb2e53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:12.076429Z","signature_b64":"nhyzNJyhEqm1bT3zaQZGtBbr4MPrD/Dedxnb/21AI5DemSO5ZIsw/wecljDt5LDAzLYhXZkay7xxvzGducBsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5f006d2f3ccd8545602494a26b72ab31c7719c47eb02ceb4fb99264f211e8c1","last_reissued_at":"2026-05-18T04:31:12.075712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:12.075712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical independent sets and Konig--Egervary graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Eugen Mandrescu, Vadim E. Levit","submitted_at":"2009-06-25T15:09:41Z","abstract_excerpt":"Let alpha(G) be the cardinality of a independence set of maximum size in the graph G, while mu(G) is the size of a maximum matching. G is a Konig--Egervary graph if its order equals alpha(G) + mu(G). The set core(G) is the intersection of all maximum independent sets of G (Levit & Mandrescu, 2002). The number def(G)=|V(G)|-2*mu(G) is the deficiency of G (Lovasz & Plummer, 1986). The number d(G)=max{|S|-|N(S)|:S in Ind(G)} is the critical difference of G. An independent set A is critical if |A|-|N(A)|=d(G), where N(S) is the neighborhood of S (Zhang, 1990). In 2009, Larson showed that G is Koni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4609","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0906.4609","created_at":"2026-05-18T04:31:12.075827+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.4609v2","created_at":"2026-05-18T04:31:12.075827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.4609","created_at":"2026-05-18T04:31:12.075827+00:00"},{"alias_kind":"pith_short_12","alias_value":"2XYANUXTZTMF","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"2XYANUXTZTMFIVQC","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"2XYANUXT","created_at":"2026-05-18T12:25:58.018023+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/2XYANUXTZTMFIVQCJFFCNNZKWM","json":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM.json","graph_json":"https://pith.science/api/pith-number/2XYANUXTZTMFIVQCJFFCNNZKWM/graph.json","events_json":"https://pith.science/api/pith-number/2XYANUXTZTMFIVQCJFFCNNZKWM/events.json","paper":"https://pith.science/paper/2XYANUXT"},"agent_actions":{"view_html":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM","download_json":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM.json","view_paper":"https://pith.science/paper/2XYANUXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.4609&json=true","fetch_graph":"https://pith.science/api/pith-number/2XYANUXTZTMFIVQCJFFCNNZKWM/graph.json","fetch_events":"https://pith.science/api/pith-number/2XYANUXTZTMFIVQCJFFCNNZKWM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM/action/storage_attestation","attest_author":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM/action/author_attestation","sign_citation":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM/action/citation_signature","submit_replication":"https://pith.science/pith/2XYANUXTZTMFIVQCJFFCNNZKWM/action/replication_record"}},"created_at":"2026-05-18T04:31:12.075827+00:00","updated_at":"2026-05-18T04:31:12.075827+00:00"}