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
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
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
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
On context-free sets of graphs and their monadic second-order theory
Proceedings of the 3rd International Workshop on Graph-Grammars and Their Application to 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
The Tutte Polynomial for Matroids of Bounded Branch-Width
Combinatorics, Probability and Computing
Trees, grids, and MSO decidability: from graphs to matroids
Theoretical Computer Science - Parameterized and exact computation
Approximating rank-width and clique-width quickly
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
The Tutte Polynomial for Matroids of Bounded Branch-Width
Combinatorics, Probability and Computing
Trees, grids, and MSO decidability: from graphs to matroids
Theoretical Computer Science - Parameterized and exact computation
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
Excluding a planar graph from GF(q)-representable matroids
Journal of Combinatorial Theory Series B
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
Computing representations of matroids of bounded branch-width
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Finding branch-decompositions and rank-decompositions
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Monadic second-order model-checking on decomposable matroids
Discrete Applied Mathematics
On matroid representability and minor problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Decomposition width of matroids
Discrete Applied Mathematics
Deciding first order properties of matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Computability of width of submodular partition functions
European Journal of Combinatorics
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
| Hi-index | 0.00 |
We introduce "matroid parse trees" which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounded branch-width over a finite field. We prove that if M is a family of matroids described by a sentence in the monadic second-order logic of matroids, then there is a finite tree automaton accepting exactly those parse trees which build vector representations of the bounded-branch-width representable members of MSince the cycle matroids of graphs are representable over any field, our result directly extends the so called "MS2-theorem" for graphs of bounded tree-width by Courcelle, and others. Moreover, applications and relations in areas other than matroid theory can be found, like for rank-width of graphs, or in the coding theory.