A Collection of Results on Saturation Number

Abstract

A graph $G$ is $H$-saturated if $G$ does not contain $H$ as a subgraph, but the addition of any edge between two nonadjacent vertices in $G$ results in a copy of $H$ in $G$. The saturation number $\mathrm{sat}(n,H)$ is the smallest possible number of edges in an $n$-vertex $H$-saturated graph. The values of saturation numbers for small graphs and $H$ are obtained computationally, and some general results for specific path unions are also obtained.