Separating systems and oriented graphs of diameter two


We prove results on the size of weakly and strongly separating set systems and matrices, and on cross-intersecting systems. As a consequence, we improve on a result of Katona and Szemerédi [G. Katona, E. Szemerédi, On a problem of graph theory, Studia Sci. Math. Hungar. 2 (1967) 23-28], who proved that the minimal number of edges in an oriented graph of order n with diameter 2 is at least (n / 2) log2 (n / 2). We show that the minimum is (1 + o (1)) n log2 n. © 2006 Elsevier Inc. All rights reserved.

Publication Title

Journal of Combinatorial Theory. Series B