{"paper":{"title":"An upper bound for the size of a $k$-uniform intersecting family with covering number $k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrii Arman, Troy Retter","submitted_at":"2016-04-16T03:50:00Z","abstract_excerpt":"Let $r(k)$ denote the maximum number of edges in a $k$-uniform intersecting family with covering number $k$. Erd\\H{o}s and Lov\\'asz proved that $ \\lfloor k! (e-1) \\rfloor \\leq r(k) \\leq k^k.$ Frankl, Ota, and Tokushige improved the lower bound to $r(k) \\geq \\left( k/2 \\right)^{k-1}$, and Tuza improved the upper bound to $r(k) \\leq (1-e^{-1}+o(1))k^k$. We establish that $ r(k) \\leq (1 + o(1)) k^{k-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04686","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"}