Weak saturation numbers for multiple copies

For a fixed graph F , a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F inG+e. Theminimumnumber of edges in an F-saturated graph of order nwill be denoted by sat(n, F). A graph G is weakly F-saturated if G contains no copy of F and there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F . The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs of order n that are weakly F-saturatedwill be denoted bywSAT(n, F), and those graphs inwSAT(n, F)withwsat(n, F) edges will be denoted bywSAT(n, F). The precise value ofwsat(n, F) for many families of vertex disjoint copies of connected graphs such as small order graphs, trees, cycles, and complete graphs will be determined. © 2014 Elsevier B.V. All rights reserved.