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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 wedoi:10.1109/sfcs.1994.365708 dblp:conf/focs/AlonFW94 fatcat:mzicu4cyfvdhpmtm77gtr65ak4