Polynomial Time Randomized Approximation Schemes for Tutte-Gröthendieck Invariants: The Dense Case

@article{Alon1994PolynomialTR,
  title={Polynomial Time Randomized Approximation Schemes for Tutte-Gr{\"o}thendieck Invariants: The Dense Case},
  author={Noga Alon and Alan M. Frieze and Dominic Welsh},
  journal={Random Struct. Algorithms},
  year={1994},
  volume={6},
  pages={459-478}
}
The Tutte-Gröthendieck polynomial T (G;x, y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x, y) plane give the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper k-colorings, the (all terminal) reliability probability of the graph, and various other invariants the exact computation of each of which is well known to be #P -hard. Here we… CONTINUE READING
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