{"paper":{"title":"A characterization of hypergraphs that achieve equality in the Chv\\'{a}tal-McDiarmid Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian L\\\"owenstein, Michael A. Henning","submitted_at":"2014-01-20T10:25:07Z","abstract_excerpt":"For $k \\ge 2$, let $H$ be a $k$-uniform hypergraph on $n$ vertices and $m$ edges. The transversal number $\\tau(H)$ of $H$ is the minimum number of vertices that intersect every edge. Chv\\'{a}tal and McDiarmid [Combinatorica 12 (1992), 19--26] proved that $\\tau(H)\\le ( n + \\left\\lfloor \\frac k2 \\right\\rfloor m )/ ( \\left\\lfloor \\frac{3k}2 \\right\\rfloor )$. When $k = 3$, the connected hypergraphs that achieve equality in the Chv\\'{a}tal-McDiarmid Theorem were characterized by Henning and Yeo [J. Graph Theory 59 (2008), 326--348]. In this paper, we characterize the connected hypergraphs that achi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4851","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"}