The tutte polynomial for matroids of bounded branch-width

Combinatorics Probability and Computing

Volumn 15, Issue 3, 2006, Pages 397-409

  Hliněný, Petr ^a,b  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

^b VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY; POLYNOMIALS; RECURSIVE FUNCTIONS; TREES (MATHEMATICS);

GRAPHIC MATROIDS; POLYNOMIAL TIME; RECURSIVE FORMULA; TUTTE POLYNOMIAL;

MATRIX ALGEBRA;

EID: 33645667803     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548305007297     Document Type: Article

References (14)

1. Andrzejak, A. (1998) An algorithm for the Tutte polynomials of graphs of bounded treewidth. Discrete Math. 190 39-54.
2. Bodlaender, H. L. and Thilikos, D. M. (1997) Constructive linear time algorithms for branch-width. In Proc. 24th ICALP, Vol. 1256 of Lecture Notes in Computer Science, Springer, pp. 627-637.
3. Downey, R. G. and Fellows, M. R. (1999) Parametrized Complexity, Springer, New York.
4. Hliněný, P. (2005) Branch-width, parse trees, and monadic second-order logic for matroids. J. of Combinatorial Theory ser. B, to appear.
5. Hliněný, P. (2005) A parametrized algorithm for matroid branch-width. SIAM J. Computing 35, 259-277 (electronic).
6. Hliněný, P. (2005) On some hard problems on matroid spikes. Theory of Computing Systems, accepted.
7. Jaeger, F., Vertigan, D. L. and Welsh, D. J. A. (1990) On the computational complexity of the Jones and Tutte polynomials. Math. Proc. Comb. Phil. Soc. 108 35-53.
8. Makowsky, J. A. (2005) Colored Tutte polynomials and Kauffman brackets for graphs of bounded tree width. Discrete Applied Mathematics 145, 276-290.
9. Noble, S. D. (1998) Evaluating the Tutte polynomial for graphs of bounded tree-width. Combin. Probab. Comput. 1 307-321.
10. Oxley, J. G. (1992, 1997) Matroid Theory, Oxford University Press.
11. Tutte, W. T (1947) A ring in graph theory. Proc. Camb. Phil. Soc. 43 26-40.
12. Vertigan, D. L. and Welsh, D. J. A. (1992) The computational complexity of the Tutte plane: the bipartite case. Combin. Probab. Comput. 1 181-187.
13. Welsh, D. J. A. (1999) The Tutte polynomial. Random Struct. Alg. 15 210-228.
14. Welsh, D. J. A. (1976) Matroid Theory, Academic Press, London.