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# Minimal Separators

Published:1999-09-01
Printed: Sep 1999
• Norbert Polat
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## Abstract

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.
 MSC Classifications: 05C40 - Connectivity