{"paper":{"title":"Duality and Hereditary K\\\"onig-Egerv\\'ary Set-systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adi Jarden","submitted_at":"2017-04-09T18:05:11Z","abstract_excerpt":"A K\\\"onig-Egerv\\'ary graph is a graph $G$ satisfying $\\alpha(G)+\\mu(G)=|V(G)|$, where $\\alpha(G)$ is the cardinality of a maximum independent set and $\\mu(G)$ is the matching number of $G$. Such graphs are those that admit a matching between $V(G)-\\bigcup \\Gamma$ and $\\bigcap \\Gamma$ where $\\Gamma$ is a set-system comprised of maximum independent sets satisfying $|\\bigcup \\Gamma'|+|\\bigcap \\Gamma'|=2\\alpha(G)$ for every set-system $\\Gamma' \\subseteq \\Gamma$; in order to improve this characterization of a K\\\"onig-Egerv\\'ary graph, we characterize \\emph{hereditary K\\\"onig-Egerv\\'ary set-systems}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02636","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":""},"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"}