Theory of linear and integer programming
Theory of linear and integer programming
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Upper bounds on the maximal of facets of 0/1-polytopes
European Journal of Combinatorics - Special issue on combinatorics of polytopes
European Journal of Combinatorics - Special issue on combinatorics of polytopes
On the Expansion of Combinatorial Polytopes
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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We introduce revlex-initial O/1-polytopes as the convex hulls of reverse-lexicographically initial subsets of 0/1-vectors. These polytopes are special knapsack-polytopes. It turns out that they have remarkable extremal properties. In particular, we use these polytopes in order to prove that the minimum numbers gnfac(d, n) of facets and the minimum average degree gavdeg(d, n) of the graph of a d-dimensional 0/1-polytope with n vertices satisfy gnfac(d, n) ≤ 3d and gavdeg(d, n) ≤ d + 4. We furthermore show that, despite the sparsity of their graphs, revlex-initial 0/1-polytopes satisfy a conjecture due to Mihail and Vazirani, claiming that the graphs of 0/1-polytopes have edge-expansion at least one.