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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.
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[5] M. A. Perles, Unpublished notes.
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