Issue |
RAIRO-Oper. Res.
Volume 58, Number 2, March-April 2024
|
|
---|---|---|
Page(s) | 2015 - 2027 | |
DOI | https://doi.org/10.1051/ro/2024071 | |
Published online | 03 May 2024 |
Some existence theorems on path-factor critical avoidable graphs
1
School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
2
School of Mathematics and Information Sciences, Yantai University, Yantai, Shandong 264005, P.R. China
* Corresponding author: zsz_cumt@163.com
Received:
7
November
2023
Accepted:
17
March
2024
A spanning subgraph F of G is called a path factor if every component of F is a path of order at least 2. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which every component has at least k vertices. A graph G is called a P≥k-factor avoidable graph if for any e ∈ E(G), G has a P≥k-factor avoiding e. A graph G is called a (P≥k, n)-factor critical avoidable graph if for any W ⊆ V (G) with |W| = n, G − W is a P≥k-factor avoidable graph. In other words, G is (P≥k, n)-factor critical avoidable if for any W ⊆ V (G) with |W| = n and any e ∈ E(G − W ), G − W − e admits a P≥k-factor. In this article, we verify that (i) an (n + r + 2)-connected graph G is (P≥2, n)-factor critical avoidable if I(G)>(n+r+2)/(2(r+2)) ; (ii) an (n + r + 2)-connected graph G is (P≥3, n)-factor critical avoidable if t(G)>(n+r+2)/(2(r+2)) ; (iii) an (n + r + 2)-connected graph G is (P≥3, n)-factor critical avoidable if I(G)>(n+3(r+2))/(2(r+2)) ; where n and r are two nonnegative integers.
Mathematics Subject Classification: 05C70 / 05C38 / 90B10
Key words: Graph / toughness / isolated toughness / connectivity / (P≥k, n)-factor critical avoidable graph
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.