# Symmetry Matters for Sizes of Extended Formulations

@article{Kaibel2012SymmetryMF,
title={Symmetry Matters for Sizes of Extended Formulations},
author={Volker Kaibel and Kanstantsin Pashkovich and Dirk Oliver Theis},
journal={SIAM J. Discret. Math.},
year={2012},
volume={26},
pages={1361-1382}
}
• Published 18 September 2012
• Mathematics
• SIAM J. Discret. Math.
In 1991, Yannakakis [J. Comput. System Sci., 43 (1991), pp. 441--466] proved that no symmetric extended formulation for the matching polytope of the complete graph $K_n$ with $n$ nodes has a number of variables and constraints that is bounded subexponentially in $n$. Here, symmetric means that the formulation remains invariant under all permutations of the nodes of $K_n$. It was also conjectured by Yannakakis that “asymmetry does not help much,” but no corresponding result for general extended…

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