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 Szemer´edi [6], 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.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Béla Bollobás, Alex D. Scott
• Keywords: Cross-intersecting Systems, JCT 2007, Separating Set, Systems