A bound for the number of vertices of a polytope with applications

Details A bound for the number of vertices of a polytope with applications A bound for the number of vertices of a polytope with applications

2011-08-14

arxiv.org/abs/1108.2871v2

Mathematics

Combinatorics

9 pages, various improvements

Scientific paper

We prove that the number of vertices of a polytope of a particular kind is exponentially large in the dimension of the polytope. As a corollary, we prove that an n-dimensional centrally symmetric polytope with O(n) facets has 2^{Omega(n)} vertices and that the number of r-factors in a k-regular graph is exponentially large in the number of vertices of the graph provided k >2r and every cut in the graph with at least two vertices on each side has more than k/r edges.

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