#3-Regular Bipartite Planar Vertex Cover is #P-Complete
We generalize the polynomial interpolation method by giving a sufficient condition, which guarantees that the coefficients of a polynomial are uniquely determined by its values on a recurrence sequence. Using this method, we show that #3-Regular Bipartite Planar Vertex Cover is #P-complete. The result is unexpected, since the same question for 2-regular graph is in FP.
KeywordsPolynomial Time Vertex Cover Main Lemma Counting Problem Linear Equation System
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