Branchwidth of chordal graphs

Authors:
Christophe Paul;Jan Arne Telle
Affiliations:
CNRS, LIRMM, 161 rue Ada, 34392 Montpellier Cedex 2, France;Department of Informatics, University of Bergen, Norway
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 11
Cited 1

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ESA'05 Proceedings of the 13th annual European conference on Algorithms
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WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science

Reduced clique graphs of chordal graphs

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Abstract

This paper revisits the 'branchwidth territories' of Kloks, Kratochvil and Muller [T. Kloks, J. Kratochvil, H. Muller, New branchwidth territories, in: 16th Ann. Symp. on Theoretical Aspect of Computer Science, STACS, in: Lecture Notes in Computer Science, vol. 1563, 1999, pp. 173-183] to provide a simpler proof, and a faster algorithm for computing the branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running time. Compliance with the ternary constraint of the branchwidth definition is facilitated by a simple new tool called k-troikas: three sets of size at most k each are a k-troika of set S, if any two have union S. We give a straightforward O(m+n+q^2) algorithm, computing branchwidth for an interval graph on m edges, n vertices and q maximal cliques. We also prove a conjecture of Mazoit [F. Mazoit, A general scheme for deciding the branchwidth, Technical Report RR2004-34, LIP - Ecole Normale Superieure de Lyon, 2004. http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-34.pdf], by showing that branchwidth can be computed in polynomial time for a chordal graph given with a clique tree having a polynomial number of subtrees.