Saturation Numbers for Linear Forests P₇+tP₂

2024/08/13 by Yu Zhang, Zhang, Yu, Rong‐Xia Hao +5 · 1 citation
Computer Science · Mathematics · #05C35 #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2408.06719

openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a fixed graph, a graph G is H-saturated if it has no copy of H in G, but the addition of any edge in E( G) to G results in an H-subgraph. The saturation number sat(n,H) is the minimum number of edges in an H-saturated graph on n vertices. In this paper, we determine the saturation number sat(n,P₇+tP₂) for n≥ \frac 145t+27 and characterize the extremal graphs for n≥ (14)/(13)(3t+25).

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