{"paper":{"title":"Bicoloring covers for graphs and hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Sudebkumar Prasant Pal, Tapas Kumar Mishra","submitted_at":"2015-01-02T04:11:11Z","abstract_excerpt":"Let the {\\it bicoloring cover number $\\chi^c(G)$} for a hypergraph $G(V,E)$ be the minimum number of bicolorings of vertices of $G$ such that every hyperedge $e\\in E$ of $G$ is properly bicolored in at least one of the $\\chi^c(G)$ bicolorings. We investigate the relationship between $\\chi^c(G)$, matchings, hitting sets, $\\alpha(G)$(independence number) and $\\chi(G)$ (chromatic number). We design a factor $O(\\frac{\\log n}{\\log \\log n-\\log \\log \\log n})$ approximation algorithm for computing a bicoloring cover. We define a new parameter for hypergraphs - \"cover independence number $\\gamma(G)$\" a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00343","kind":"arxiv","version":4},"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"}