math.CO

Title: Saturation Numbers for Linear Forests $P_6$ + $tP_2$

Authors: Jingru Yan
Abstract: A graph $G$ is $H$-saturated if it has no $H$ as a subgraph, but does contain $H$ after the addition of any edge in the complement of $G$. The saturation number, sat$(n,H)$, is the minimum number of edges of a graph in the set of all H-saturated graphs with order $n$. In this paper, we determine the saturation number sat$(n, P_6 + tP_2)$ for $n\ge 10t/3 + 10$ and characterize the extremal graphs for $n > 10t/3 + 20$.
 Comments: 11 pages, 1 figure Subjects: Combinatorics (math.CO) MSC classes: 05C35, 05C38 Cite as: arXiv:2106.06466 [math.CO] (or arXiv:2106.06466v1 [math.CO] for this version)

Submission history

From: Jingru Yan [view email]
[v1] Fri, 11 Jun 2021 15:38:05 GMT (9kb)
[v2] Sun, 17 Oct 2021 05:03:07 GMT (9kb)

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