Saturation numbers for linear forests

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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Publication Details

Journal
Springer Link (Chiba Institute of Technology)
Published
2026-07-16
DOI
https://doi.org/10.1051/ro/2026073/pdf
Primary Topic
Limits and Structures in Graph Theory
Type
article
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article

Saturation numbers for linear forests

Renying Chang, Xueliang Li
Springer Link (Chiba Institute of Technology)
Limits and Structures in Graph Theory
article

Saturation numbers for linear forests

Renying Chang, Xueliang Li
article en

Abstract

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.

Springer Link (Chiba Institute of Technology)
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Limits and Structures in Graph Theory
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