BIPARTITE PERFECT MATCHING AS A REAL POLYNOMIAL

被引：0

作者：

Beniamini, Gal ^{[1
]}

Nisan, Noam ^{[1
]}

机构：

[1] Hebrew Univ Jerusalem, Sch Comp Sci & Engn, IL-91904 Jerusalem, Israel

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2023年 / 256卷 / 01期

基金：

欧洲研究理事会;

关键词：

D O I：

10.1007/s11856-023-2505-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a description of the Bipartite PerfectMatching decision problem as a multilinear polynomial over the Reals. We show that it has full total degree and (1- o(1))center dot 2(n2) 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.

引用

页码：91 / 131

页数：41

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