{"paper":{"title":"Hereditary Konig Egervary Collections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adi Jarden","submitted_at":"2016-03-21T19:36:16Z","abstract_excerpt":"Let $G$ be a simple graph with vertex set $V(G)$. A subset $S$ of $V(G)$ is independent if no two vertices from $S$ are adjacent. The graph $G$ is known to be a Konig-Egervary (KE in short) graph 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. Let $\\Omega(G)$ denote the family of all maximum independent sets. A collection $F$ of sets is an hke collection if $|\\bigcup \\Gamma|+|\\bigcap \\Gamma|=2\\alpha$ holds for every subcollection $\\Gamma$ of $F$. We characterize an hke collection and invoke "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06552","kind":"arxiv","version":3},"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"}