{"paper":{"title":"Generalized Hypergraph Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas Schweser","submitted_at":"2018-04-17T16:06:43Z","abstract_excerpt":"A smooth hypergraph property $\\mathcal{P}$ is a class of hypergraphs that is hereditary and non-trivial, i.e., closed under induced subhypergraphs and it contains a non-empty hypergraph but not all hypergraphs. In this paper we examine $\\mathcal{P}$-colorings of hypergraphs with smooth hypergraph properties $\\mathcal{P}$. A $\\mathcal{P}$-coloring of a hypergraph $H$ with color set $C$ is a function $\\varphi:V(H) \\to C$ such that $H[\\varphi^{-1}(c)]$ belongs to $\\mathcal{P}$ for all $c \\in C$. Let $L: V(H) \\to 2^C$ be a so called list-assignment of the hypergraph $H$. Then, a $(\\mathcal{P},L)$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06338","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"}