{"paper":{"title":"Some properties and applications of odd-colorable $r$-hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chen Ouyang, Jiayu Shao, Liqun Qi, Xiying Yuan","submitted_at":"2016-06-16T03:59:56Z","abstract_excerpt":"Let $r\\geq2$ and $r$ be even. An $r$-hypergraph $G$ on $n$ vertices is called odd-colorable if there exists a map $\\varphi:[n]\\rightarrow\\lbrack r]$ such that for any edge $\\{j_{1},j_{2},\\cdots,j_{r}\\}$ of $G$, we have $\\varphi(j_{1})+\\varphi(j_{2})+\\cdot\\cdot\\cdot+\\varphi(j_{r})\\equiv r/2(\\operatorname{mod}r).$ In this paper, we first determine that, if $r=2^{q}(2t+1)$ and $n\\ge 2^{q}(2^{q}-1)r$, then the maximum chromatic number in the class of the odd-colorable $r$-hypergraphs on $n$ vertices is $2^q$, which answers a question raised by V. Nikiforov recently in [V. Nikiforov, Hypergraphs an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05045","kind":"arxiv","version":4},"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"}