Some hard problems on matroid spikes

Theory of Computing Systems

Volumn 41, Issue 3, 2007, Pages 551-562

  Hlineny, Petr ^a,b  

^a VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

^b MASARYK UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL PROBLEM; FINITE FIELDS; HARD PROBLEMS; INFINITE FIELDS; MATRIX REPRESENTATION; MONADIC SECOND-ORDER LOGIC; TUTTE POLYNOMIAL;

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

GRAPH THEORY;

EID: 36849080745     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-007-1307-5     Document Type: Conference Paper

References (16)

1. B. Courcelle, The Monadic Second-Order Logic of Graphs I. Recognizable Sets of Finite Graphs, Inform. Comput. 85 (1990), 12-75.
2. R.G. Downey, M.R. Fellows, Parametrized Complexity, Springer-Verlag New York, 1999.
3. M.R. Garey, D.S. Johnson, Computers and Intractability, Freeman, New York, 1979.
4. J.F. Geelen, A.H.M. Gerards, G.P. Whittle, Branch-Width and Well-Quasi-Ordering in Matroids and Graphs, J. Combin. Theory Ser. B 84 (2002), 270-290.
5. P. Hliněný, The Tutte Polynomial for Matroids of Bounded Branch-Width, Combin. Probab. Comput. 15 (2006), 397-409.
6. P. Hliněný, Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids, J. Combin. Theory Ser. B 96 (2006), 325-351.
7. P. Hliněný, A Parametrized Algorithm for Matroid Branch-Width, SIAMJ. Comput. 35 (2005), 259-277 (electronic).
8. P. Hliněný, D. Seese, Trees, Grids, and MSO Decidability: from Graphs to Matroids, Theoret. Comput. Sci. 351 (2006), 372-393.
9. P. Hliněný, On matroid representability and minor problems, Proceedings MECS 2006, Lecture Notes in Computer Science 4162, Springer, Berlin, 2006, pp. 505-516.
10. F. Jaeger, D.L. Vertigan, D.J.A. Welsh, On the Computational Complexity of the Jones and Tutte Polynomials, Math. Proc. Cambridge Philos. Soc. 108 (1990), 35-53.
11. D. Mayhew, Matroids and Complexity, D.Phil. Thesis, University of Oxford, 2005.
12. S.D. Noble, Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width, Combin. Probab. Comput. 7 (1998), 307-321.
13. J.G. Oxley, Matroid Theory, Oxford University Press, Oxford, 1992, 1997.
14. J.G. Oxley, D. Vertigan, G. Whittle, On Inequivalent Representations of Matroids over Finite Fields, J. Combin. Theory Set: B 67 (1996), 325-343.
15. W.T. Tutte, A Ring in Graph Theory, Math. Proc. Cambridge Philos. Soc. 43 (1947), 26-40.
16. L.G. Valiant, The Complexity of Enumeration and Reliability Problems, SIAM J. Comput. 8 (1979), 410-421.