Author:
Zhou Sizhong,Bian Qiuxiang
Abstract
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.
Subject
Management Science and Operations Research,Computer Science Applications,Theoretical Computer Science
Cited by
15 articles.
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