Abstract
Minimal triangulations and potential maximal cliques are the main ingredients for a number of polynomial time algorithms on different graph classes computing the treewidth of a graph. Potential maximal cliques are also the main engine of the fastest so far \(\mathcal{O}\)(1.9601n)-time exact treewidth algorithm. Based on the recent results of Mazoit, we define the structures that can be regarded as minimal triangulations and potential maximal cliques for branchwidth: efficient triangulations and blocks. We show how blocks can be used to construct an algorithm computing the branchwidth of a graph on n vertices in time (2 + \(\sqrt{\rm 3}\))\(^{\it n}\) · n O(1).
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Fomin, F., Mazoit, F., Todinca, I. (2005). Computing Branchwidth Via Efficient Triangulations and Blocks. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_33
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DOI: https://doi.org/10.1007/11604686_33
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