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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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
- General Position
- Pairwise Disjoint
- Discrete Comput Geom
- Straight Line Segment
- Geometric Graph