Volume 55, Number 3, May-June 2021
|Page(s)||1279 - 1290|
|Published online||19 May 2021|
Isolated toughness and path-factor uniform graphs
School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
2 School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210046, P.R. China
3 School of Mathematics and Informational Science, Yantai University, Yantai, Shandong 264005, P.R. China
* Corrresponding author: firstname.lastname@example.org
Accepted: 11 April 2021
A P≥k-factor of a graph G is a spanning subgraph of G whose components are paths of order at least k. We say that a graph G is P≥k-factor covered if for every edge e ∈ E(G), G admits a P≥k-factor that contains e; and we say that a graph G is P≥k-factor uniform if for every edge e ∈ E(G), the graph G−e is P≥k-factor covered. In other words, G is P≥k-factor uniform if for every pair of edges e1, e2 ∈ E(G), G admits a P≥k-factor that contains e1 and avoids e2. In this article, we testify that (1) a 3-edge-connected graph G is P≥k-factor uniform if its isolated toughness I(G) > 1; (2) a 3-edge-connected graph G is P≥k-factor uniform if its isolated toughness I(G) > 2. Furthermore, we explain that these conditions on isolated toughness and edge-connectivity in our main results are best possible in some sense.
Mathematics Subject Classification: 05C70 / 05C38 / 90B10
Key words: Graph / isolated toughness / edge-connectivity / path-factor / path-factor uniform graph
© EDP Sciences, ROADEF, SMAI 2021
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