{"paper":{"title":"Improved Inapproximability of Rainbow Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Aditya Potukuchi, Amey Bhangale, Per Austrin","submitted_at":"2018-10-05T16:39:43Z","abstract_excerpt":"A rainbow $q$-coloring of a $k$-uniform hypergraph is a $q$-coloring of the vertex set such that every hyperedge contains all $q$ colors.\n  We prove that given a rainbow $(k - 2\\lfloor \\sqrt{k}\\rfloor)$-colorable $k$-uniform hypergraph, it is NP-hard to find a normal $2$-coloring. Previously, this was only known for rainbow $\\lfloor k/2 \\rfloor$-colorable hypergraphs (Guruswami and Lee, SODA 2015).\n  We also study a generalization which we call rainbow $(q, p)$-coloring, defined as a coloring using $q$ colors such that every hyperedge contains at least $p$ colors. We prove that given a rainbow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02784","kind":"arxiv","version":3},"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"}