Star Saturation Number of Random Graphs

Abstract

For a given graph $F$, the $F$-saturation number of a graph $G$ is the minimum number of edges in an edge-maximal $F$-free subgraph of $G$. Recently, the $F$-saturation number of the Erd\H{o}s$\text{\bf--}$R\'enyi random graph $\mathbbmsl{G}(n, p)$ has been determined asymptotically for any complete graph $F$. In this paper, we give an asymptotic formula for the $F$-saturation number of $\mathbbmsl{G}(n, p)$ when $F$ is a star graph.