Binding number conditions for [formula omitted]-factor and [formula omitted]-factor uniform graphs

Abstract

Let k≥2 be an integer, and let G be a graph. A spanning subgraph F of a graph G is called a P≥k-factor of G if each component of F is a path of order at least k. We present the definition of a P≥k-factor uniform graph, i.e., for any two distinct edges e1 and e2 of G, G admits a P≥k-factor including e1 and excluding e2. We give two binding number conditions for a graph to be a P≥2-factor uniform graph and a P≥3-factor uniform graph.