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Minimal Separators

Published online by Cambridge University Press:  20 November 2018

Norbert Polat
Norbert Polat*
Affiliation:
I. A. E., Université Jean Moulin (Lyon 3) 15, quai Claude Bernard 69239 Lyon Cedex 2 France, email: polat@jonas.univ-lyon1.fr
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Abstract

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A separator of a connected graph $G$ is a set of vertices whose removal disconnects $G$. In this paper we give various conditions for a separator to contain a minimal one. In particular we prove that every separator of a connected graph that has no thick end, or which is of bounded degree, contains a minimal separator.

Keywords

05C40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 386 - 392
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Polat, N., Ends and multi-endings, I. J. Combin. Theory Ser. B 67 (1996), 86–110.Google Scholar
[2] Sabidussi, G., Minimal isthmoids. Monatsh.Math. 66 (1962), 346–350.Google Scholar