This research characterizes minimum edges for linear forests in saturated graphs, suggesting critical properties of graph structures.
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 ∉ 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.
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Chang et al. (2025) studied this question.
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