Factor criticality and complete closure of graphs

A graph G is said to be n-factor-critical if G-T has a perfect matching for every [email protected]?V(G) with |T|=n. For a vertex x of a graph G, local completion of G at x is the operation of joining every pair of nonadjacent vertices in N"G(x). For a property P of graphs, a vertex x in a graph G is said to be P-eligible if the subgraph of G induced by N"G(x) satisfies P but it is not complete. For a graph G, a graph H is said to be a P-closure of G if there exists a series of graphs G=G"0,G"1,...,G"r=H such that G"i is obtained from G"i"-"1 by local completion at some P-eligible vertex in G"i"-"1 and H=G"r has no P-eligible vertex. In this paper, we investigate the relation between factor-criticality and a P-closure, where P is a bounded independence number or a bounded domination number.