English

Saturation Numbers for Linear Forests $P_7+tP_2$

Combinatorics 2024-08-14 v1

Abstract

Let HH be a fixed graph, a graph G is HH-saturated if it has no copy of HH in GG, but the addition of any edge in E(G)E(\overline G) to GG results in an HH-subgraph. The saturation number sat(n,H)(n,H) is the minimum number of edges in an HH-saturated graph on nn vertices. In this paper, we determine the saturation number sat(n,P7+tP2)(n,P_7+tP_2) for n145t+27n\geq \frac {14}{5}t+27 and characterize the extremal graphs for n1413(3t+25)n\geq \frac{14}{13}(3t+25).

Keywords

Cite

@article{arxiv.2408.06719,
  title  = {Saturation Numbers for Linear Forests $P_7+tP_2$},
  author = {Yu Zhang and Rong-Xia Hao and Zhen He and Wen-Han Zhu},
  journal= {arXiv preprint arXiv:2408.06719},
  year   = {2024}
}

Comments

11 pages

R2 v1 2026-06-28T18:11:27.279Z