{"paper":{"title":"On the generalized Erd\\H{o}s--Kneser conjecture: proofs and reductions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ethan Coldren, Florian Frick, Jai Aslam, Linus Setiabrata, Shuli Chen","submitted_at":"2017-12-10T00:23:36Z","abstract_excerpt":"Alon, Frankl, and Lov\\'asz proved a conjecture of Erd\\H{o}s that one needs at least $\\lceil \\frac{n-r(k-1)}{r-1} \\rceil$ colors to color the $k$-subsets of $\\{1, \\dots, n\\}$ such that any $r$ of the $k$-subsets that have the same color are not pairwise disjoint. A generalization of this problem where one requires $s$-wise instead of pairwise intersections was considered by Sarkaria. He claimed a proof of a generalized Erd\\H{o}s--Kneser conjecture establishing a lower bound for the number of colors that reduces to Erd\\H{o}s' original conjecture for ${s = 2}$. Lange and Ziegler pointed out that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03456","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"}