{"paper":{"title":"On Chromatic Number of Kneser Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","submitted_at":"2013-02-21T20:07:53Z","abstract_excerpt":"In this paper, in view of $Z_p$-Tucker lemma, we introduce a lower bound for chromatic number of Kneser hypergraphs which improves Dol'nikov-K{\\v{r}}{\\'{\\i}}{\\v{z}} bound. Next, we introduce multiple Kneser hypergraphs and we specify the chromatic number of some multiple Kneser hypergraphs. For a vector of positive integers $\\vec{s}=(s_1,s_2,\\ldots,s_m)$ and a partition $\\pi=(P_1,P_2,\\ldots,P_m)$ of $\\{1,2,\\ldots,n\\}$, the multiple Kneser hypergraph ${\\rm KG}^r(\\pi; \\vec{s};k)$ is a hypergraph with the vertex set $$V=\\left\\{A:\\ A\\subseteq P_1\\cup P_2\\cup\\cdots \\cup P_m,\\ |A|=k, \\forall 1\\leq i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5394","kind":"arxiv","version":2},"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"}