{"paper":{"title":"Choosability with separation of complete multipartite graphs and hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Mohit Kumbhat, Zolt\\'an F\\\"uredi","submitted_at":"2011-09-14T02:14:09Z","abstract_excerpt":"For a hypergraph G and a positive integer s, let \\chi_{\\ell} (G,s) be the minimum value of l such that G is L-colorable from every list L with |L(v)|=l for each v\\in V(G) and |L(u)\\cap L(v)|\\leq s for all u, v\\in e\\in E(G). This parameter was studied by Kratochv\\'{i}l, Tuza and Voigt for various kinds of graphs. Using randomized constructions we find the asymptotics of \\chi_{\\ell} (G,s) for balanced complete multipartite graphs and for complete k-partite k-uniform hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2969","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"}