Extremal problems for triple systems

In this article Turán-type problems for several triple systems arising from (k, k ? 2)-configurations [i.e. (k ? 2) triples on k vertices] are considered. It will be shown that every Steiner triple system contains a (k, k ? 2)-configuration for some k < c log n/ log log n. Moreover, the Turán numbers of (k, k ? 2)-trees are determined asymptotically to be ((k ? 3)/3).(ⁿ₂) (1?o(1)). Finally, anti-Pasch hypergraphs avoiding (5, 3) -and (6, 4)-Configurations are considered. © 1993 John Wiley & Sons, Inc.