A counterexample to Borsuk’s conjecture

Jeff Kahn, Gil Kalai

Research output: Contribution to journalComment/debate

133 Scopus citations

Abstract

Let f(d) be the smallest number so that every set in Rd of diameter 1 can be partitioned into f(d) sets of diameter smaller than 1. Borsuk’s conjecture was that f(d) = d+1. We prove that f(d) ≥ (1.2)(Equation presented) for large d.

Original languageEnglish
Pages (from-to)60-62
Number of pages3
JournalBulletin of the American Mathematical Society
Volume29
Issue number1
DOIs
StatePublished - Jul 1993

Fingerprint

Dive into the research topics of 'A counterexample to Borsuk’s conjecture'. Together they form a unique fingerprint.

Cite this