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The Computational Complexity of the Tutte Plane: the Bipartite Case

  • D. L. Vertigan (a1) and D. J. A. Welsh (a2)

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.

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[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.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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