Volume 56, Number 4, July-August 2022
|Page(s)||2919 - 2927|
|Published online||30 August 2022|
The existence of path-factor uniform graphs with large connectivity
School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 9 August 2022
A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor covering e. A graph G is called a P≥k-factor uniform graph if for any e1, e2 ∈ E(G) with e1 ≠ e2, G has a P≥k-factor covering e1 and avoiding e2. In other words, a graph G is called a P≥k-factor uniform graph if for any e ∈ E(G), G − e is a P≥k-factor covered graph. In this paper, we present two sufficient conditions for graphs to be P≥3-factor uniform graphs depending on binding number and degree conditions. Furthermore, we show that two results are best possible in some sense.
Mathematics Subject Classification: 05C70 / 05C38
Key words: Graph / degree condition / binding number / P≥3-factor / P≥3-factor uniform graph
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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.