Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
Branch-width and well-quasi-ordering in matroids and graphs
Journal of Combinatorial Theory Series B
Problems Easy for Tree-Decomposable Graphs (Extended Abstract)
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
The Tutte Polynomial for Matroids of Bounded Branch-Width
Combinatorics, Probability and 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
On Rota's conjecture and excluded minors containing large projective geometries
Journal of Combinatorial Theory Series B
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Journal of Combinatorial Theory Series B
Excluding a planar graph from GF(q)-representable matroids
Journal of Combinatorial Theory Series B
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Addendum to matroid tree-width
European Journal of Combinatorics
Tangles, tree-decompositions and grids in matroids
Journal of Combinatorial Theory Series B
Computing representations of matroids of bounded branch-width
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On matroid representability and minor problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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Hlineny [P. Hlineny, Branch-width, parse trees, and monadic second-order logic for matroids, J. Combin. Theory Ser. B 96 (2006), 325-351] showed that every matroid property expressible in the monadic second-order logic can be decided in linear time for matroids with bounded branch-width that are represented over finite fields. To be able to extend these algorithmic results to matroids not representable over finite fields, we introduce a new width parameter for matroids, the decomposition width, and show that every matroid property expressible in the monadic second-order logic can be computed in linear time for matroids given by a decomposition with bounded width. We also relate the decomposition width to matroid branch-width and discuss implications of our results with respect to known algorithms.