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

Ryjáček 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 ∈ { H , P i , N i , j , k } .