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Minimal vertex separators of chordal graphs

Kumar, P Sreenivasa and Madhavan, C E Veni (1998) Minimal vertex separators of chordal graphs. In: Discrete Applied Mathematics, 89 (1-3). pp. 155-168.

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Chordal graphs form an important and widely studied subclass of perfect graphs. The set of minimal vertex separators constitute an unique class of separators of a chordal graph and capture the structure of the graph. In this paper, we explore the connection between perfect elimination orderings of a chordal graph and its minimal vertex separators. Specifically, we prove a characterization of these separators in terms of the monotone adjacency sets of the vertices of the graph, numbered by the maximum cardinality search (MCS) scheme. This leads to a simple linear-time algorithm to identify the minimal vertex separators of a chordal graph using the MCS scheme. We also introduce the notion of multiplicity of a minimal vertex separator which indicates the number of different pairs of vertices separated by it. We prove a useful property of the lexicographic breadth first scheme (LBFS) that enables us to determine the multiplicities of minimal vertex separators of a chordal graph.

Item Type: Journal Article
Publication: Discrete Applied Mathematics
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: chordal graphs;minimal vertex separators;maximum cardinality search;lexicographic breadth first search.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 18 Dec 2009 11:59
Last Modified: 19 Sep 2010 05:26
URI: http://eprints.iisc.ac.in/id/eprint/18950

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