The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
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
Parameterized Complexity
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Decomposition width of matroids
Discrete Applied Mathematics
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We introduce "matroid parse trees" which, using only a limited amount of information, can build up all matroids of bounded branch-width representable over a finite field. We prove that if M is a family of matroids described by a sentence in the second-order monadic logic of matroids, then the parse trees of bounded-width representable members of M can be recognized by a finite tree automaton. Since the cycle matroids of graphs are representable over any finite field, our result directly extends the well-known "MS2-theorem" for graphs of bounded tree-width by Courcelle and others. This work has algorithmic applications in matroid or coding theories.