Article ID Journal Published Year Pages File Type
4649267 Discrete Mathematics 2010 8 Pages PDF
Abstract

Ryjáček introduced a closure concept for claw-free graphs based on local completion of a locally connected vertex. Connected graphs AA, for which the class of (C,A)(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)(C,A)-free graphs is stable under the edge-closure if A∈{H,Pi,Ni,j,k}A∈{H,Pi,Ni,j,k}.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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