{"paper":{"title":"Fair representation by independent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dani Kotlar, Eli Berger, Maria Chudnovsky, Martin Loebl, Noga Alon, Ran Ziv, Ron Aharoni","submitted_at":"2016-11-10T06:31:33Z","abstract_excerpt":"For a hypergraph $H$ let $\\beta(H)$ denote the minimal number of edges from $H$ covering $V(H)$. An edge $S$ of $H$ is said to represent {\\em fairly} (resp. {\\em almost fairly}) a partition $(V_1,V_2, \\ldots, V_m)$ of $V(H)$ if $|S\\cap V_i|\\ge \\lfloor\\frac{|V_i|}{\\beta(H)}\\rfloor$ (resp. $|S\\cap V_i|\\ge \\lfloor\\frac{|V_i|}{\\beta(H)}\\rfloor-1$) for all $i \\le m$.\n  In matroids any partition of $V(H)$ can be represented fairly by some independent set. We look for classes of hypergraphs $H$ in which any partition of $V(H)$ can be represented almost fairly by some edge.\n  We show that this is true"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03196","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"}