Matching properties in domination critical graphs

A graph G is said to be k-gamma-critical if the size of any minimum dominating set of vertices is k, but if any edge is added to G the resulting graph can be dominated with k-1 vertices. A graph G is factor-critical if G-v has a perfect matching for every vertex v epsilon V(G) and is bicritical if G-u-v has a perfect matching for every pair of distinct vertices u, v epsilon V(G). In the present paper, it is shown that under certain assumptions regarding connectivity and minimum degree, a 3-gamma-critical graph G will be either factor-critical (if \V(G)\ is odd) or bicritical (if \V(G)\ is even). (C) 2003 Elsevier B.V. All rights reserved.