A Characterization of Homothetic Simplices |
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| Authors: | V Soltan |
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| Institution: | (1) Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic valtr@kam.ms.mff.cuni.cz and DIMACS Center, Rutgers University, P.O. Box 1179, Piscataway, NJ 08855, USA valtr@dimacs.rutgers.edu, US |
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| Abstract: | For any k we construct a simply connected compact set (art gallery) in R
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whose every point sees a positive fraction (in fact, more than 5/9) of the gallery, but the whole gallery cannot be guarded
by k guards. This disproves a conjecture of Kavraki et al.
Received May 2, 1997, and in revised form February 5, 1998. |
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