AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 40 (2008), Pages 211–215 A note on minimum K 2,3 -saturated graphs Oleg Pikhurko * Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213-3890 U.S.A. John Schmitt Department of Mathematics Middlebury College Middlebury, VT 05753 U.S.A. jschmitt@middlebury.edu Abstract A graph G is said to be K 2,3 -saturated if G contains no copy of K 2,3 as a subgraph, but for any edge e in the complement of G the graph G + e does contain a copy of K 2,3 . The minimum number of edges of a K 2,2 - saturated graph of given order n was precisely determined by Ollmann in 1972. Here, we determine the asymptotic behavior for the minimum number of edges in a K 2,3 -saturated graph. 1 Introduction We denote the complete graph on t vertices by K t , and the complete bipartite graph with partite sets of size a and b by K a,b . We let G =(V,E) be a graph on |V | = n vertices and |E| edges. The graph G is said to be F -saturated if G contains no copy of F as a subgraph, but for any edge e in the complement of G, the graph G + e contains a copy of F , where G + e denotes the graph (V,E ∪{e}). For a graph F we will denote the minimum size of an F -saturated graph by sat(n, F ). In 1964 Erd˝os, Hajnal and Moon [3] determined sat(n, K t ) for all n, t. Determining the exact value of this function for a given graph F is quite difficult in general, and the * Partially supported by the National Science Foundation, Grant DMS-0457512.