On 0-1 Polytopes with Many Facets

There exist n-dimensional 0-1 polytopes with as many as (cn/logn)(n/4) facets. This is our main result. It answers a question of Komei Fukuda and Gunter M. Ziegler. (C) 2001 Academic Press.

[1]  T. Bonnesen,et al.  Theorie der Konvexen Körper , 1934 .

[2]  Anton E. Mayer.  Theorie der konvexen Körper , 1936 .

[3]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[4]  Some near-sphericity results , 1963 .

[5]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[6]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[7]  R. Tichy,et al.  Stochastical approximation of convex bodies , 1985 .

[8]  Zoltán Füredi,et al.  Computing the volume is difficult , 1986, STOC '86.

[9]  Computing the volume is difficult , 1987, Discret. Comput. Geom..

[10]  B. Carl,et al.  Gelfand numbers of operators with values in a Hilbert space , 1988 .

[11]  Micha Sharir,et al.  The caratheodory number for thek-core , 1990, Comb..

[12]  Martin E. Dyer,et al.  Volumes Spanned by Random Points in the Hypercube , 1992, Random Struct. Algorithms.

[13]  J. Eckhoff.  Helly, Radon, and Carathéodory Type Theorems , 1993 .

[14]  Jörg M. Wills,et al.  Handbook of Convex Geometry , 1993 .

[15]  Michel Deza,et al.  Geometry of cuts and metrics , 2009, Algorithms and combinatorics.

[16]  Günter M. Ziegler,et al.  Extremal Properties of 0/1-Polytopes , 1997, Discret. Comput. Geom..

[17]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[18]  G. Ziegler,et al.  Polytopes : combinatorics and computation , 2000 .

[19]  G. Ziegler.  Lectures on 0/1-Polytopes , 1999, math/9909177.

[20]  Günter Rote,et al.  Upper Bounds on the Maximal Number of Facets of 0/1-Polytopes , 2000, Eur. J. Comb..