The Characterization ofp-factor-critical Graphs

• 作者: Shao-hui ZHAI Er-ling WEI Fu-ji ZHANG
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 154-158
• 页数: 5页
• 语种: 英文

摘要

A graph G is said to be p-factor-critical if G-u1-u2-…-up has a perfect matching for any u1,u2,…,up ∈ V(G).The concept of p-factor-critical is a generalization of the concepts of factor-critical and bicritical for p=1 and p=2,respectively.Heping Zhang and Fuji Zhang[Construction for bicritical graphs and k-extendable bipartite graphs,Discrete Math.,306(2006)1415-1423]gave a concise structure characterization of bicritical graphs.In this paper,we present the characterizations of p-factor-critical graphs and minimal p-factor-critical graphs for p≥2.As an application,we also obtain a class of graphs which are minimal p-factor-critical for p≥1.