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

  title={Polynomial Time Randomised Approximation Schemes for Tutte-Gr{\"o}thendieck Invariants: The Dense Case},
  author={Noga Alon and Alan M. Frieze and Dominic J. A. Welsh},
  journal={Electron. Colloquium Comput. Complex.},
The Tutte‐Grothendieck 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… 

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