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The number d(X)= |X|-|N(X)| is the difference of X, and an independent set A is critical if d(A) = max{d(I):I is an independent set in G} (Zhang; 1990). Let Omega(G) denote the family of all maximum independent sets. Let us say that a family Gamma of independent sets is a Konig-Egervary collection if |Unio"},"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":"1512.01994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T11:45:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f76b4261bcd7e58db58d19c729e2c754220d4d349382eedee3621e9c3782cbc5","abstract_canon_sha256":"4d6dbab2c523517bc86f423548ddfc953d893415f840a984589826ed7234e04c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:09.848806Z","signature_b64":"odHRTGUASHRa7a93IL6eg4hlA6q9l+rIZZHqMsU33ij5FPB+lZyg74/ZTM8qsk6xxoD8jAdgTNfmipkyJQAbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c99cf10152e959cdd5bac2f60c75d3eee76487bd75f830df9806b3826b362530","last_reissued_at":"2026-05-18T01:25:09.848277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:09.848277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Konig-Egervary Collections of Maximum Critical Independent Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Eugen Mandrescu, Vadim E. Levit","submitted_at":"2015-12-07T11:45:02Z","abstract_excerpt":"Let G be a simple graph with vertex set V(G). A set S is independent if no two vertices from S are adjacent. The graph G is known to be a Konig-Egervary if alpha(G)+mu(G)= |V(G)|, where alpha(G) denotes the size of a maximum independent set and mu(G) is the cardinality of a maximum matching. The number d(X)= |X|-|N(X)| is the difference of X, and an independent set A is critical if d(A) = max{d(I):I is an independent set in G} (Zhang; 1990). Let Omega(G) denote the family of all maximum independent sets. 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