{"paper":{"title":"Chromatic-choosability of hypergraphs with high chromatic number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianguo Qian, Wei Wang","submitted_at":"2018-07-22T11:27:38Z","abstract_excerpt":"It was conjectured by Ohba and confirmed recently by Noel et al. that, for any graph $G$, if $|V(G)|\\le 2\\chi(G)+1$ then $\\chi_l(G)=\\chi(G)$. This indicates that the graphs with high chromatic number are chromatic-choosable. We show that this is also the case for uniform hypergraphs and further propose a generalized version of Ohba's conjecture: for any $r$-uniform hypergraph $H$ with $r\\geq 2$, if $|V(H)|\\le r\\chi(H)+r-1$ then $\\chi_l(H)=\\chi(H)$. We show that the condition of the proposed conjecture is sharp by giving two classes of $r$-uniform hypergraphs $H$ with $|V(H)|= r\\chi(H)+r$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08273","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"}