3-Factor-criticality in domination critical graphs

A graph G is factor-critical if G-v has a perfect matching for every vertex v∈V(G) and is bicritical if G-u-v has a perfect matching for every pair of distinct vertices u,v∈V(G). More generally, a graph is said to be k-factor-critical if G-S has a perfect matching for every set S of k vertices in G. In three previous papers [N. Ananchuen, M.D. Plummer, Some results related to the toughness of 3-domination-critical graphs, Discrete Math. 272 (2003) 5-15; N. Ananchuen, M.D. Plummer, Matching properties in domination critical graphs, Discrete Math. 277 (2004) 1-13; N. Ananchuen, M.D. Plummer, Some results related to the toughness of 3-domination-critical graphs. II. Utilitas Math. 70 (2006) 11-32], we explored the toughness of 3-γ-critical graphs and some of their matching properties. In particular, we obtained some properties which are sufficient for a 3-γ-critical graph to be factor-critical and, respectively, bicritical. In the present work, we obtain similar results for k-factor-critical graphs when k=3.