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The illumination conjecture and its extensions

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Summary

The Illumination Conjecture was raised independently by Boltyanski and Hadwiger in 1960. According to this conjecture any <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>d$-dimensional convex body can be illuminated by at most $2^d$ light sources. This is an important fundamental problem. The paper surveys the state of the art of the Illumination Conjecture.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary & Department of Geometry Eötvös Loránd University, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada & Pázmány Péter sétány 1/c H-1117 Budapest, Hungary

    Károly Bezdek

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  1. Károly Bezdek
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Bezdek, K. The illumination conjecture and its extensions. Period Math Hung 53, 59–69 (2006). https://doi.org/10.1007/s10998-006-0021-4

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  • DOI: https://doi.org/10.1007/s10998-006-0021-4

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