{"paper":{"title":"The chromatic number of 3-stable Kneser graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Parker, Shira Zerbib, Wei-Chia Chen","submitted_at":"2026-07-14T15:48:41Z","abstract_excerpt":"For an integer $s \\ge 2$, a subset $S \\subseteq [n]$ is {\\em $s$-stable} if $\\min \\{j - i, n + i - j\\}\\ge s$ for every $i,j \\in S$ with $i<j$. Denote the set of all $s$-stable subsets of size $k$ of $[n]$ by $\\binom{[n]}{k}_{s\\text{-stable}}$. Schrijver proved in 1978 that whenever $n\\ge 2k$, the chromatic number of the Kneser graph $\\mathrm{KG}\\big( \\binom{[n]}{k}_{2\\text{-stable}}\\big)$ is $n - 2k +2$. Generalizing this result, Meunier conjectured in 2011 that $\\chi\\left( \\mathrm{KG}\\big( \\binom{[n]}{k}_{s\\text{-stable}} \\big) \\right)= n - sk +s$ for all $n\\ge sk$. This conjecture was previo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12912","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12912/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}