Weak saturation numbers of and

Abstract

A graph is weakly -saturated if contains no copy of , and there is an ordering of all edges of so that if they are added one at a time, they form a complete graph and each edge added creates a new copy of . The minimum size of a weakly -saturated graph of order is weak saturation number, denoted by . Let denote the complete graph with vertices, denote the complete bipartite graph with partite sizes of and , and denote the complement of . In this paper, we determine and whose significance can be seen in the introduction.

Keywords

• weakly saturated graph
• weak saturation number
• complete graph
• complete bipartite graph