Branch-width, parse trees, and monadic second-order logic for matroids

Journal of Combinatorial Theory. Series B

Volumn 96, Issue 3, 2006, Pages 325-351

  Hliněný, Petr ^a  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

Branch width; Fixed parameter complexity; Matroid representation; Monadic second order logic; Tree automaton

Indexed keywords

EID: 33645920646     PISSN: 00958956     EISSN: 10960902     Source Type: Journal    
DOI: 10.1016/j.jctb.2005.08.005     Document Type: Article

References (26)

1. K.A. Abrahamson, M.R. Fellows, Finite Automata, bounded treewidth, and well-quasiordering, in: Graph Structure Theory, Contemporary Mathematics, vol. 147, American Mathematical Society, 1993, pp. 539-564.
2. S. Arnborg, J. Lagergren, D. Seese, Problems easy for tree-decomposible graphs (extended abstract), Proceedings of the 15th Colloq. Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 317, Springer, Berlin, 1988, pp. 38-51.
3. Bodlaender H.L. A tourist guide through treewidth. Acta Cybernetica 11 (1993) 1-21
4. H.L. Bodlaender, D.M. Thilikos, Constructive linear time algorithms for branchwidth, Proceedings 24th ICALP, Lecture Notes in Computer Science, vol. 1256, 1997, pp. 627-637.
5. Borie R.B., Parker R.G., and Tovey C.A. Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families. Algorithmica 7 (1992) 555-582
6. B. Courcelle, On context-free sets of graphs and their monadic second-order theory, in: Graph-Grammars and Their Application to Computer Science, Proceedings of the International Workshop on Graph Grammars 1986, Lecture Notes in Computer Science, vol. 291, 1987, pp. 133-146.
7. Courcelle B. The monadic second-order logic of graphs I. Recognizable sets of finite graphs. Inform. and Comput. 85 (1990) 12-75
8. Courcelle B., Makowsky J.A., and Rotics U. Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Systems 33 (2000) 125-150
9. Courcelle B., and Olariu S. Upper bounds to the clique width of graphs. Discrete Appl. Math. 101 (2000) 77-114
10. B. Courcelle, Sang-Il Oum, Vertex-minors, monadic second-order logic, and a conjecture by Seese, 2005, submitted for publication.
11. Downey R.G., and Fellows M.R. Parametrized Complexity (1999), Springer, New York
12. Geelen J.F., Gerards A.H.M., Robertson N., and Whittle G.P. On the excluded minors for the matroids of branch-width k. J. Combin. Theory Ser. B 88 (2003) 261-265
13. Geelen J.F., Gerards A.H.M., and Whittle G.P. Branch-width and well-quasi-ordering in matroids and graphs. J. Combin. Theory Ser. B 84 (2002) 270-290
14. J.F. Geelen, A.H.M. Gerards, G.P. Whittle, Excluding a Planar Graph from a GF ( q )-Representable Matroid, manuscript, 2003.
15. P. Hliněný, On Some Hard Problems on Matroid Spikes, submitted (2005).
16. P. Hliněný, On matroid properties definable in the MSO logic, in: Math Foundations of Computer Science MFCS 2003, Lecture Notes in Computer Science, vol. 2747, Springer, Berlin, 2003, pp. 470-479.
17. P. Hliněný, The tutte polynomial for matroids of bounded branch-width, combinatorics, Probab. Comput., 2005, to appear.
18. P. Hliněný, A parametrized algorithm for matroid branch-width, SIAM J. Comput., 2005, to appear.
19. P. Hliněný, D. Seese, Trees, grids, and MSO decidability: from graphs to matroids, Theoret. Computer Sci., 2005, to appear. (Extended abstract in: IWPEC 2004, Lecture Notes in Computer Science, vol. 3162, Springer, Berlin, 2004, pp. 96-107.)
20. P. Hliněný, G.P. Whittle, Matroid Tree-Width, submitted for publication. Ext. abstract in: Eurocomb'03, ITI Series 2003-145, Charles University 2003.
21. Oxley J.G. Matroid Theory (1992), Oxford University Press, Oxford
22. N. Robertson, P.D. Seymour, Graph Minors-A Survey, Surveys in Combinatorics, Cambridge University Press, Cambridge, 1985, pp. 153-171.
23. Robertson N., and Seymour P.D. Graph minors X. obstructions to tree-decomposition. J. Combin. Theory Ser. B 52 (1991) 153-190
24. Sang-Il Oum, P.D. Seymour, Approximation Algorithm to the Clique-Width of a Graph, 2004, submitted for publication.
25. Sang-Il Oum, Approximating Rank-width and Clique-width Quickly, in: Proceedings WG 2005, Lecture Notes in Computer Science 3787 (2005), Springer Verlag, to appear.
26. Seese D. The structure of models of decidable monadic theories of graphs. Ann. Pure Appl. Logic 53 (1991) 169-195