Bipartite perfect matching as a real polynomial

Gal Beniamini*, Noam Nisan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We obtain a description of the Bipartite Perfect Matching decision problem as a multilinear polynomial over the Reals. We show that it has full total degree and (1−o(1))⋅2n2 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 Θ(n log n). Our proof relies heavily on the fact that the lattice of graphs which are “matching-covered” is Eulerian.

Original languageAmerican English
Pages (from-to)91-131
Number of pages41
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Sep 2023

Bibliographical note

Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.


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