The Tuza–Vestergaard Theorem
Michael A. Henning, Christian Löwenstein, Anders Yeo · SIAM Journal on Discrete Mathematics · 2023
Abstract. The transversal number [Formula: see text] of a hypergraph [Formula: see text] is the minimum number of vertices that intersect every edge of [Formula: see text]. A 6-uniform hypergraph has all edges of size 6. On 10 November 2000 Tuza and Vestergaard [ Discuss. Math. Graph Theory, 22 (2002), pp. 199–210] conjectured that if [Formula: see text] is a 3-regular 6-uniform hypergraph of order [Formula: see text], then [Formula: see text]. In this paper we prove this conjecture, which has become known as the Tuza–Vestergaard conjecture.