Abstract. 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 Ω(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+1 and every cut in the graph with at least two vertices on each side has more than k/r edges. 1. Introduction an
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