Steiner systems and large non-Hamiltonian hypergraphs

Abstract

From Steiner systems <em>S(k − 2, 2k − 3, v)</em>, we construct <em>k</em>-uniform hyper- graphs of large size without Hamiltonian cycles. This improves previous estimates due to G. Y. Katona and H. Kierstead [J. Graph Theory 30 (1999), pp. 205–212].<br />