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arXiv · 2001.07642

Bipartite Perfect Matching as a Real Polynomial

Gal Beniamini·Noam Nisan
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Abstract

We obtain a description of the Bipartite Perfect Matching decision problem as a multilinear polynomial over the Reals. We show that it has full degree and $(1-o_n(1))\cdot 2^{n^2}$ monomials with non-zero coefficients. In contrast, we show that in the dual representation (switching the roles of 0 and 1) the number of monomials is only exponential in $\Theta(n \log n)$. Our proof relies heavily on the fact that the lattice of graphs which are "matching-covered" is Eulerian.

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Gal Beniamini, Noam Nisan. 2020-01-21. Bipartite Perfect Matching as a Real Polynomial. https://arxiv.org/abs/2001.07642

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