Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 23
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Aksoy, Sinan and Horn, Paul 2016. Graphs with Many Strong Orientations. SIAM Journal on Discrete Mathematics, Vol. 30, Issue. 2, p. 1269.


    Gong, Helin and Jin, Xian’an 2014. Potts model partition functions on two families of fractal lattices. Physica A: Statistical Mechanics and its Applications, Vol. 414, p. 143.


    Tuza, Zsolt 2013. Handbook of Graph Theory, Second Edition.


    KOTEK, TOMER 2012. Complexity of Ising Polynomials. Combinatorics, Probability and Computing, Vol. 21, Issue. 05, p. 743.


    2011. Graph Coloring Problems.


    Beaudin, Laura Ellis-Monaghan, Joanna Pangborn, Greta and Shrock, Robert 2010. A little statistical mechanics for the graph theorist. Discrete Mathematics, Vol. 310, Issue. 13-14, p. 2037.


    GEBAUER, HEIDI and OKAMOTO, YOSHIO 2009. FAST EXPONENTIAL-TIME ALGORITHMS FOR THE FOREST COUNTING AND THE TUTTE POLYNOMIAL COMPUTATION IN GRAPH CLASSES. International Journal of Foundations of Computer Science, Vol. 20, Issue. 01, p. 25.


    Valiant, Leslie G. 2008. Holographic Algorithms. SIAM Journal on Computing, Vol. 37, Issue. 5, p. 1565.


    Goodall, A.J. 2004. The Tutte polynomial modulo a prime. Advances in Applied Mathematics, Vol. 32, Issue. 1-2, p. 293.


    Grimmett, G. R. and Winkler, S. N. 2004. Negative association in uniform forests and connected graphs. Random Structures and Algorithms, Vol. 24, Issue. 4, p. 444.


    Korn, Michael and Pak, Igor 2004. Tilings of rectangles with T-tetrominoes. Theoretical Computer Science, Vol. 319, Issue. 1-3, p. 3.


    Valiant, L.G. 2004. 45th Annual IEEE Symposium on Foundations of Computer Science. p. 306.

    Welsh, Dominic and Gale, Amy 2001. Aspects of Complexity.


    Welsh, D. J. A. and Merino, C. 2000. The Potts model and the Tutte polynomial. Journal of Mathematical Physics, Vol. 41, Issue. 3, p. 1127.


    Merino, C. and Welsh, D. J. A. 1999. Forests, colorings and acyclic orientations of the square lattice. Annals of Combinatorics, Vol. 3, Issue. 2-4, p. 417.


    Welsh, Dominic 1999. The Tutte polynomial. Random Structures and Algorithms, Vol. 15, Issue. 3-4, p. 210.


    Brown, Jason I. 1998. Chromatic polynomials and order ideals of monomials. Discrete Mathematics, Vol. 189, Issue. 1-3, p. 43.


    Alon, Noga Frieze, Alan and Welsh, Dominic 1995. Polynomial time randomized approximation schemes for Tutte-Gröthendieck invariants: The dense case. Random Structures & Algorithms, Vol. 6, Issue. 4, p. 459.


    Alon, N. Frieze, A. and Welsh, D. 1994. Proceedings 35th Annual Symposium on Foundations of Computer Science. p. 24.

    Annan, J. D. 1994. A Randomised Approximation Algorithm for Counting the Number of Forests in Dense Graphs. Combinatorics, Probability and Computing, Vol. 3, Issue. 03, p. 273.


    ×
  • Combinatorics, Probability and Computing, Volume 1, Issue 2
  • June 1992, pp. 181-187

The Computational Complexity of the Tutte Plane: the Bipartite Case

  • D. L. Vertigan (a1) and D. J. A. Welsh (a2)
  • DOI: http://dx.doi.org/10.1017/S0963548300000195
  • Published online: 01 September 2008
Abstract

Along different curves and at different points of the (x, y)-plane the Tutte polynomial evaluates a wide range of quantities. Some of these, such as the number of spanning trees of a graph and the partition function of the planar Ising model, can be computed in polynomial time, others are # P-hard. Here we give a complete characterisation of which points and curves are easy/hard in the bipartite case.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[4]N. Linial (1986) Hard enumeration problems in geometry and combinatorics. SIAM J. Alg. Disc. Math. 7, 331335.

[6]L. G. Valiant (1979) The complexity of enumeration and reliability problems. SIAM J. Comput. 8, 410421.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×