A characterization of hypergraphs that achieve equality in the Chvátal-McDiarmid Theorem

For k≥2, let H be a k-uniform hypergraph on n vertices and m edges. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. Chvátal and McDiarmid (1992) proved that τ(H)≤(n+⌊k2⌋m)/(⌊3k2⌋). When k=3, the connected hypergraphs that achieve equality in the Chvátal-McDiarmid Theorem were characterized by Henning and Yeo (2008). In this paper, we characterize the connected hypergraphs that achieve equality in the Chvátal-McDiarmid Theorem for k=2 and for all k≥4.