Saturation Numbers for Linear Forests

Abstract

Given a graph $H$, we say a graph $G$ is $H$-saturated if $G$ does
not contain $H$ as a subgraph and the addition of any edge $ e
\notin E(G)$ results in $H$ as a subgraph. The question of the
minimum number of edges of an $H$-saturated graph on n vertices,
known as the $saturation$ $number$.

In this paper, we mainly research the saturation number for linear
forests and characterize the extremal graphs.