Minimum degree and the minimum size of Kt 2 - saturated graphs Ronald

A graph G is said to be F-saturated if G does not contain a copy of F as a subgraph and G+ e contains a copy of F as a subgraph for any edge e contained in the complement of G. Erdős et al. in [A problem in graph theory, Amer. Math. Monthly 71 (1964) 1107–1110.] determined the minimum number of edges, sat(n, F ), such that a graph G on n vertices must have when F is a t-clique. Later, Ollmann [K2,2-saturated graphs with a minimal number of edges, in: Proceedings of the Third SouthEast Conference on Combinatorics, Graph Theory and Computing, 1972, pp. 367–392.] determined sat(n, F ) for F = K2,2. Here we give an upper bound for sat(n, F ) when F =K2 t the complete t-partite graph with partite sets of size 2, and prove equality when G is of prescribed minimum degree. © 2006 Elsevier B.V. All rights reserved.