Constructing designs straightforwardly: Worst arising cases

Suppose that we consecutively remove edges from some k ‐graph of order n in which every t vertices are covered by at least λ edges to obtain a minimal such k ‐graph. What can be said about the size of the eventual k ‐graph? While, by the result of Rödl [Europ. J. Combin. 5 (1985), 69–78], the minimum is $\lambda {n\choose t}/{k\choose t}+o(n^t)$ , we show that the maximum is $\lambda {n\choose t}+o(n^t)$ . Also, some partial results are obtained about possible size of a maximal k ‐graph covering every t ‐set by at most λ edges. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 100–106, 2001