Star Saturation Number of Random Graphs

TL;DR

This paper derives an asymptotic formula for the star saturation number in Erdős–Rényi random graphs, extending previous results from complete graphs to star graphs.

Contribution

It provides the first asymptotic characterization of the $F$-saturation number for star graphs in random graphs.

Findings

Asymptotic formula for star saturation number in Erdős–Rényi graphs

Extension of saturation number results from complete graphs to star graphs

New insights into the structure of $F$-free subgraphs in 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.