Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
The excluded minors for GF(4)-representable matroids
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
The Inference Problem for Propositional Circumscription of Affine Formulas Is coNP-Complete
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
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
The branchwidth of graphs and their cycle matroids
Journal of Combinatorial Theory Series B
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Linear delay enumeration and monadic second-order logic
Discrete Applied Mathematics
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the inherent intractability of certain coding problems (Corresp.)
IEEE Transactions on Information Theory
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
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A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids. We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded branch-width, by reduction to monadic second-order formulas on trees. This proof is much simpler than the one previously known. We also provide a link between our logical approach and a grammar that allows one to build matroids of bounded branch-width. Finally, we introduce a new class of non-necessarily representable matroids, described by a grammar and on which monadic second-order formulas can be checked in linear time.