{"paper":{"title":"Brooks Type Results for Conflict-Free Colorings and {a, b}-factors in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Rollin, Maria Axenovich","submitted_at":"2014-10-05T22:47:53Z","abstract_excerpt":"A vertex-coloring of a hypergraph is conflict-free, if each edge contains a vertex whose color is not repeated on any other vertex of that edge. Let $f(r, \\Delta)$ be the smallest integer $k$ such that each $r$-uniform hypergraph of maximum vertex degree $\\Delta$ has a conflict-free coloring with at most $k$ colors. As shown by Tardos and Pach, similarly to a classical Brooks' type theorem for hypergraphs, $f(r, \\Delta)\\leq \\Delta+1$. Compared to Brooks' theorem, according to which there is only a couple of graphs/hypergraphs that attain the $\\Delta+1$ bound, we show that there are several inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1219","kind":"arxiv","version":2},"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"}