{"paper":{"title":"A new lower bound for the chromatic number of general Kneser hypergraphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Meysam Alishahi, Roya Abyazi Sani","submitted_at":"2017-04-24T06:23:14Z","abstract_excerpt":"A general Kneser hypergraph ${\\rm KG}^r(\\mathcal{H})$ is an $r$-uniform hypergraph that somehow encodes the edge intersections of a ground hypergraph $\\mathcal{H}$. The colorability defect of $\\mathcal{H}$ is a combinatorial parameter providing a lower bound for the chromatic number of ${\\rm KG}^r(\\mathcal{H})$ which is addressed in a series of works by Dol'nikov [Sibirskii Matematicheskii Zhurnal, 1988}], K\\v{r}\\'{\\i}\\v{z} [Transaction of the American Mathematical Society, 1992], and Ziegler~[Inventiones Mathematicae, 2002]. In this paper, we define a new combinatorial parameter, the equitabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07052","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"}