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 straight-forward O(m + n + q2) 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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Paul, C., & Telle, J. A. (2005). New tools and simpler algorithms for branchwidth. In Lecture Notes in Computer Science (Vol. 3669, pp. 379–390). Springer Verlag. https://doi.org/10.1007/11561071_35
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