{"paper":{"title":"Approximability of the upper chromatic number of hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as, Zsolt Tuza","submitted_at":"2013-10-29T20:56:02Z","abstract_excerpt":"A C-coloring of a hypergraph ${\\cal H}=(X,{\\cal E})$ is a vertex coloring $\\varphi: X\\to {\\mathbb{N}}$ such that each edge $E\\in{\\cal E}$ has at least two vertices with a common color. The related parameter $\\overline{\\chi}({\\cal H})$, called the upper chromatic number of ${\\cal H}$, is the maximum number of colors can be used in a C-coloring of ${\\cal H}$. A hypertree is a hypergraph which has a host tree $T$ such that each edge $E\\in {\\cal E}$ induces a connected subgraph in $T$. Notations $n$ and $m$ stand for the number of vertices and edges, respectively, in a generic input hypergraph.\n  "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7964","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"}