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

 Citace: HOLUB, P., BROUSEK, J. The edge-closure concept for claw-free graphs and the stability of forbidden subgraphs. Discrete Mathematics, 2010, roč. 310, č. 13-14, s. 1856-1863. ISSN: 0012-365X ČLÁNEK eng The edge-closure concept for claw-free graphs and the stability of forbidden subgraphs 2010 Amsterdam Elsevier RNDr. Přemysl Holub Ph.D. , RNDr. Jan Brousek Ph.D. 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 \in {H,Pi,Ni,j,k}.

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