The edge-closure concept for claw-free graphs and the stability of forbidden subgraphs

Ryjacek introduced a closure concept for claw-free graphs based on local completion of a locally connected vertex. Connected graphs A, for which the class of (C, A)-free graphs is stable under the closure, were completely characterized. In this paper, we introduce a variation of the closure concept based on local completion of a locally connected edge of a claw-free graph. The closure is uniquely determined and preserves the value of the circumference of a graph. We show that the class of (C, A)-free graphs is stable under the edge-closure if A is an element of {H, P-i, N-i,N-j,N-k}. (C) 2010 Elsevier B.V. All rights reserved.