Abstract
Answering an old question in combinatorial geometry, we show that any configuration consisting of a setV ofn points in general position in the plane and a set of 6n − 5 closed straight line segments whose endpoints lie inV, contains three pairwise disjoint line segments.
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J. Akiyama and N. Alon, Disjoint simplices and geometric hypergraphs,Proc. 3rd New York Conference on Combinatorial Mathematics, Annals of the New York Academy of Sciences, to appear.
S. Avital and H. Hanani, Graphs,Gilyonot Lematematika 3(2) (1966), 2–8 (in Hebrew).
P. Erdös, On sets of distances ofn points,Amer. Math. Monthly 53 (1946), 248–250.
Y. S. Kupitz,Extremal Problems in Combinatorial Geometry, Aarhus University Lecture Notes Series, No. 53, Aarhus University, Denmark, 1979.
M. A. Perles, Unpublished notes.
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Research supported in part by an Allon Fellowship and by a Bat Sheva de-Rothschild grant.
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Alon, N., Erdös, P. Disjoint edges in geometric graphs. Discrete Comput Geom 4, 287–290 (1989). https://doi.org/10.1007/BF02187731
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DOI: https://doi.org/10.1007/BF02187731