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New Tools and Simpler Algorithms for Branchwidth

Christophe Paul 1 Jan Arne Telle
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We provide new tools, such as k-troikas and good subtree-representations, that allow us to give fast and simple algorithms computing branchwidth. We show that a graph G has branchwidth at most k if and only if it is a subgraph of a chordal graph in which every maximal clique has a k-troika respecting its minimal separators. Moreover, if G itself is chordal with clique tree T then such a chordal supergraph exists having clique tree a minor of T. We use these tools to 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 F. Mazoit [13] by showing that branchwidth is polynomial on a chordal graph given with a clique tree having a polynomial number of subtrees.
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Contributor : Christine Carvalho de Matos <>
Submitted on : Monday, October 16, 2006 - 8:29:28 AM
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Christophe Paul, Jan Arne Telle. New Tools and Simpler Algorithms for Branchwidth. ESA: European Symposium on Algorithms, Oct 2005, Palma de Mallorca, Spain. pp.379-390, ⟨10.1007/11561071_35⟩. ⟨lirmm-00106466⟩



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