{"paper":{"title":"On proper colorings of hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dmitrii Karpov, Nick Gravin","submitted_at":"2011-11-07T12:27:57Z","abstract_excerpt":"Let $\\mathcal{H}$ be a hypergraph of maximal vertex degree $\\Delta$, such that each its hyperedge contains at least $\\delta$ vertices. Let $k=\\lceil\\frac{2\\Delta}{\\delta}\\rceil$. We prove that (i) The hypergraph $\\mathcal{H}$ admits proper vertex coloring in $k+1$ colors. (ii) The hypergraph $\\mathcal{H}$ admits proper vertex coloring in $k$ colors, if $\\delta\\ge 3$ and $k\\ge 3$. As a consequence of these results we derive upper bounds on the number of colors in dynamic colorings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1558","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"}