Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
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
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
Algorithm Design
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
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
New tools and simpler algorithms for branchwidth
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Computing branchwidth via efficient triangulations and blocks
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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Branchwidth is a connectivity parameter of graphs closely related to treewidth. Graphs of treewidth at most k can be generated algorithmically as the subgraphs of k-trees. n this paper, we investigate the family of edge-maximal graphs of branchwidth k, that we call k-branches. The k-branches are, just as the k-trees, a subclass of the chordal graphs where all minimal separators have size k. However, a striking difference arises when considering subgraph-minimal members of the family. Whereas Kk+1 is the only subgraph-minimal k-tree, we show that for any k ≥7 a minimal k-branch having q maximal cliques exists for any value of , except for k=8,q=2. We characterize subgraph-minimal k-branches for all values of k. Our investigation leads to a generation algorithm, that adds one or two new maximal cliques in each step, producing exactly the k-branches.