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 facto...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-factorcritical graphs for p≥2.As an application,we also obtain a class of graphs which are minimal p-factor-critical for p≥1.展开更多
基金Supported by the National Natural Science Foundation of China(No.11401576)。
文摘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-factorcritical graphs for p≥2.As an application,we also obtain a class of graphs which are minimal p-factor-critical for p≥1.
