Some results about ID-path-factor critical graphs
Zhiren Sun, Sizhong Zhou · Discrete Mathematics Letters · 2023
Let G be a graph of order n.A spanning subgraph F of G is said to be a P ≥k -factor of G if every component of F is a path with at least k vertices, where k ≥ 2. In this paper, we introduce the concept of an ID-P ≥k -factor critical graph; a graph G is said to be an ID-P ≥k -factor critical graph if for any independent set I of G, G -I admits a P ≥k -factor.We prove that a graph G of a given order is an ID-P ≥2 -factor critical graph if its binding number is at least 2. We also prove that a graph G of a fixed order is an ID-P ≥3 -factor critical graph if its binding number is at least 9 4 .Furthermore, we show that the obtained results are the best possible in some sense.