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Erschienen in:
19.11.2020 | Original Research
Toughness and isolated toughness conditions for \(P_{\ge 3}\)-factor uniform graphs
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021
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Abstract
Given a graph G and an integer \(k\ge 2\). A spanning subgraph F of a graph G is said to be a \(P_{\ge k}\)-factor of G if each component of F is a path of order at least k. A graph G is called a \(P_{\ge k}\)-factor uniform graph if for any two distinct edges \(e_{1}\) and \(e_{2}\) of G, G admits a \(P_{\ge k}\)-factor including \(e_{1}\) and excluding \(e_{2}\). More recently, Zhou and Sun (Discret Math 343:111715, 2020) gave binding number conditions for a graph to be \(P_{\ge 2}\)-factor and \(P_{\ge 3}\)-factor uniform graphs, respectively. In this paper, we present toughness and isolated toughness conditions for a graph to be a \(P_{\ge 3}\)-factor uniform graph, respectively.