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Mathematical Programming

, Volume 18, Issue 1, pp 84–88 | Cite as

Borsuk's theorem through complementary pivoting

  • Imre Bárány
Short Communication

Abstract

In this short note a simple and constructive proof is given for Borsuk's theorem on antipodal points. This is done through a special application of the complementary pivoting algorithm.

Key words

Complementary Pivot Algorithms Triangulations Vector Labels Borsuk's Theorem on Antipodal Points 

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References

  1. [1]
    I. Bárány, “A short proof of Kneser's conjecture”,Journal of Combinatorial Theory 25 (1978) 325–326.Google Scholar
  2. [2]
    K. Borsuk, “Drei Sätze über dien-dimensionalische euklidische Sphäre”,Fundamenta Mathematicae 20 (1933) 177–190.Google Scholar
  3. [3]
    F.E. Browder, “On continuity of fixed points under deformations of continuous mappings”,Summa Brasiliensis Mathematicae 4 (1960) 183–191.Google Scholar
  4. [4]
    B.C. Eaves, “A short course in solving equations with PL homotopies”SIAM-AMS Proceedings 9 (1976) 73–143.Google Scholar
  5. [5]
    L. Lovász, “Kneser's conjecture, chromatic number and homotopy”,Journal of Combinatorial Theory 25 (1978) 319–324.Google Scholar
  6. [6]
    M.J. Todd,The computation of fixed points and applications (Springer, Berlin, 1976).Google Scholar

Copyright information

© The Mathematical Programming Society 1980

Authors and Affiliations

  • Imre Bárány
    • 1
  1. 1.OTSZK, KTTBudapestHungary

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