For any two-colouring of the segments determined by 3n-3 points in general position in the plane, either the first colour class contains a triangle, or there is a noncrossing cycle of length n in the secondcolour class, and this result is tight. We also give a series of more general estimates on off-diagonal geometric graph Ramsey numbers in the same spirit. Finally we investigate the existence of large noncrossing monochromatic matchings in multicoloured geometric graphs.
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Forschungsinstitut für Mathematik, ETH Zürich preprint
Spinoza prijs Lex Schrijver
Networks and Optimization

Karolyi, G, & Rosta, V. (2007). On geometric graph Ramsey numbers. Forschungsinstitut für Mathematik, ETH Zürich preprint. FIM.