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Algorithms 2010, 3(2), 100-124; doi:10.3390/a3020100

Graph Extremities Defined by Search Algorithms

1,* , 2
3 and 3
1 LIMOS, Université Blaise Pascal, Ensemble scientifique des Cézeaux, F-63177 Aubière, France 2 Department of EE & CS, United States Military Academy, West Point, NY 10996, USA 3 LIRMM, 161, Rue Ada, F-34392 Montpellier, France
* Author to whom correspondence should be addressed.
Received: 1 January 2010 / Revised: 9 February 2010 / Accepted: 22 February 2010 / Published: 24 March 2010
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Graph search algorithms have exploited graph extremities, such as the leaves of a tree and the simplicial vertices of a chordal graph. Recently, several well-known graph search algorithms have been collectively expressed as two generic algorithms called MLS and MLSM. In this paper, we investigate the properties of the vertex that is numbered 1 by MLS on a chordal graph and by MLSM on an arbitrary graph. We explain how this vertex is an extremity of the graph. Moreover, we show the remarkable property that the minimal separators included in the neighborhood of this vertex are totally ordered by inclusion.
Keywords: graph search; graph extremity; LexBFS; MCS; MLS graph search; graph extremity; LexBFS; MCS; MLS
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Berry, A.; Blair, J.R.; Bordat, J.-P.; Simonet, G. Graph Extremities Defined by Search Algorithms. Algorithms 2010, 3, 100-124.

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