Unit squares intersecting all secants of a square |
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| Authors: | Pavel Valtr |
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| Institution: | 1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic
2. Graduiertenkolleg “Algorithmische Diskrete Mathematik”, Fachbereich Mathematik, Freie Universit?t Berlin, Arnimallee 2-6, 1000, Berlin 33, Germany
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| Abstract: | LetS be a square of side lengths>0. We construct, for any sufficiently larges, a set of less than 1.994s closed unit squares whose sides are parallel to those ofS such that any straight line intersectingS intersects at least one square ofS. It disproves L. Fejes Tóth's conjecture that, for integrals, there is no such configuration of less than 2s−1 unit squares.
Supported by “Deutsche Forschungsgemeinschaft”, Grant We 1265/2-1. |
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