{"paper":{"title":"Chromatic Numbers of Simplicial Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Frank H. Lutz, Jesper M. M{\\o}ller","submitted_at":"2015-03-28T00:48:04Z","abstract_excerpt":"Higher chromatic numbers $\\chi_s$ of simplicial complexes naturally generalize the chromatic number $\\chi_1$ of a graph. In any fixed dimension $d$, the $s$-chromatic number $\\chi_s$ of $d$-complexes can become arbitrarily large for $s\\leq\\lceil d/2\\rceil$ [6,18]. In contrast, $\\chi_{d+1}=1$, and only little is known on $\\chi_s$ for $\\lceil d/2\\rceil<s\\leq d$.\n  A particular class of $d$-complexes are triangulations of $d$-manifolds. As a consequence of the Map Color Theorem for surfaces [29], the 2-chromatic number of any fixed surface is finite. However, by combining results from the literat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08251","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"}