Saturation numbers for linear forests P4 ∪ P3 ∪ tP2

Abstract

For a fixed graph F, a graph G is F-saturated if it has no F as a subgraph, but for any edge e ϵ E(G), there is a copy of F in G + e. The saturation number, sat(n, F), is the minimum number of edges of a graph in the set of all F-saturated graphs with order n. In this paper, we determine the saturation number sat(n, P₄ ∪ P₃ ∪ tP₂) and characterize the extremal graphs for n ≥ 6t + 22.