How to guard a museum

  • Martin Aigner
  • Günter M. Ziegler

Abstract

Here is an appealing problem which was raised by Victor Klee in 1973. Suppose the manager of a museum wants to make sure that at all times every point of the museum is watched by a guard. The guards are stationed at fixed posts, but they are able to turn around. How many guards are needed?

Keywords

Hull 

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References

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    V. Chvátal: A combinatorial theorem in plane geometry, J. Combinatorial Theory, Ser. B 18 (1975), 39–41.MathSciNetMATHCrossRefGoogle Scholar
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    S. Fisk: A short proof of Chvátal’s watchman theorem, J. Combinatorial Theory, Ser. B 24 (1978), 374.MathSciNetMATHCrossRefGoogle Scholar
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    J. O’Rourke: Art Gallery Theorems and Algorithms, Oxford University Press 1987.Google Scholar
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    E. Schönhardt: Über die Zerlegung von Dreieckspolyedern in Tetraeder, Math. Annalen 98 (1928), 309–312.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, MA 6-2Technische Universität BerlinBerlinGermany

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