A note on intersecting hypergraphs with large cover number (Q2401407)

Summary: We give a construction of \(r\)-partite \(r\)-uniform intersecting hypergraphs with cover number at least \(r-4\) for all but finitely many \(r\). This answers a question of \textit{A. Abu-Khazneh} et al. [``A family of extremal hypergraphs for Ryser's conjecture'', Preprint, \url{arXiv:1605.06361}], and shows that a long-standing unsolved conjecture due to \textit{H. J. Ryser} [``Neuere Probleme der Kombinatorik'', in: Vortrage über Kombinatorik, Ober-Wolfach, Mathematisches Forschungsinstitut Oberwolfach, 24--29 (1967)] is close to being best possible for every value of \(r\).