Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649267 | Discrete Mathematics | 2010 | 8 Pages |
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
Authors
Jan Brousek, Přemysl Holub,