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Upper Bound on the Number of Vertices of Polyhedra with $0,1$-Constraint Matrices

Khaled Elbassioni·Zvi Lotker·Raimund Seidel
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Abstract

In this note we show that the maximum number of vertices in any polyhedron $P=\{x\in \mathbb{R}^d : Ax\leq b\}$ with $0,1$-constraint matrix $A$ and a real vector $b$ is at most $d!$.

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Khaled Elbassioni, Zvi Lotker, Raimund Seidel. 2005-07-14. Upper Bound on the Number of Vertices of Polyhedra with $0,1$-Constraint Matrices. https://arxiv.org/abs/cs/0507038

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