Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graphs with branchwidth at most three
Journal of Algorithms
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
Computing the branchwidth of interval graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Journal of Computer and System Sciences
Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Computing branchwidth via efficient triangulations and blocks
Discrete Applied Mathematics
Discrete Applied Mathematics
Mixed search number and linear-width of interval and split graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Generation of graphs with bounded branchwidth
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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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+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.