Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
On the excluded minors for the matroids of branch-width k
Journal of Combinatorial Theory Series B
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
Journal of Combinatorial Theory Series B
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
The branchwidth of graphs and their cycle matroids
Journal of Combinatorial Theory Series B
Approximating rank-width and clique-width quickly
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Efficient First-Order Model-Checking Using Short Labels
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Graph operations characterizing rank-width
Discrete Applied Mathematics
Linear delay enumeration and monadic second-order logic
Discrete Applied Mathematics
Graph operations characterizing rank-width and balanced graph expressions
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most k if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parameter tractable, that is, they run in time O(n3) for each fixed value of k where n is the number of vertices / elements of the input. (The previous best algorithm for construction of a branch-decomposition or a rank-decomposition of optimal width due to Oum and Seymour [Testing branch-width. J. Combin. Theory Ser. B, 97(3) (2007) 385-393] is not fixed-parameter tractable).