Some old and new problems in combinatorial geometry I: Around Borsuk's problem

2015/05/19 by Gil Kalai, Kalai, Gil · 2 citations
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #Limits and Structures in Graph Theory #cs.CG #math.CO #math.MG

paper · pdf · doi:10.48550/arxiv.1505.04952

This is a draft of a chapter for "Surveys in Combinatorics 2015," edited by Artur Czumaj, Angelos Georgakopoulos, Daniel Kral, Vadim Lozin, and Oleg Pikhurko. The final published version shall be available for purchase from Cambridge University Press

arxiv created 2015/05/19 · arxiv updated 2015/05/20

Abstract

Borsuk asked in 1933 if every set of diameter 1 in R^d can be covered by d+1 sets of smaller diameter. In 1993, a negative solution, based on a theorem by Frankl and Wilson, was given by Kahn and Kalai. In this paper I will present questions related to Borsuk's problem.

Citations

• A 64-dimensional two-distance counterexample to Borsuk's conjecture
• On Borsuk's conjecture for two-distance sets

Cited by

• Forbidden vector-valued intersections
• Conic optimization for extremal geometry

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• An elementary proof of borsuk theorem
• A Computer Program for Borsuk's Conjecture
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• Topological Borsuk problem