Mathematical analysis identifies saturation numbers for linear forests, aiding graph theory insights.
We say that G is F-$saturated$ if G contains no copy of F and for all e ∈ E(Ḡ) the graph $G + e$ does contain a copy of F. The saturation number, denote by $sat(n,F)$, is the minimum size of a graph with order n in all F-saturated graphs. In this paper, we determine the saturation numbers for linear forests P₅ ∪ P₄ ∪ tP₂ and characterize the extremal graphs.
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Chang et al. (2026) studied this question.
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