Saturation Numbers for Linear Forests $P_6$ + $t{P}_2$

Abstract

A graph $G$ is $H$-saturated if it contains no $H$ as a subgraph, but does contain $H$ after the addition of any edge in the complement of $G$. The saturation number, $sat(n,H)$, is the minimum number of edges of a graph in the set of all $H$-saturated graphs with order $n$. In this paper, we determine the saturation number $sat(n,P_6+t{P}_2)$ for $n\ge 10t/3+10$ and characterize the extremal graphs for $n>10t/3+20$.

11 pages, 1 figure