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Disjoint edges in geometric graphs. (English) Zbl 0692.05037

Summary: Answering an old question in combinatorial geometry, we show that any configuration consisting of a set \(V\) of \(n\) points in general position in the plane and a set of \(6n-5\) closed straight line segments whose endpoints lie in \(V\), contains three pairwise disjoint line segments.

MSC:

05C35 Extremal problems in graph theory
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References:

[1] 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. · Zbl 0734.05064
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[3] P. Erdös, On sets of distances ofn points,Amer. Math. Monthly53 (1946), 248-250. · Zbl 0060.34805 · doi:10.2307/2305092
[4] Y. S. Kupitz,Extremal Problems in Combinatorial Geometry, Aarhus University Lecture Notes Series, No. 53, Aarhus University, Denmark, 1979. · Zbl 0414.05029
[5] M. A. Perles, Unpublished notes.
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