# On Geometric Graph Ramsey Numbers

@article{Krolyi2009OnGG, title={On Geometric Graph Ramsey Numbers}, author={Gyula K{\'a}rolyi and Vera Rosta}, journal={Graphs and Combinatorics}, year={2009}, volume={25}, pages={351-363} }

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 second colour 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.

## 2 Citations

### Ramsey-Type Problems for Geometric Graphs

- Mathematics
- 2013

We survey some results and collect a set of open problems related to graph Ramsey theory with geometric constraints.

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Note: Professor Pach's number: [065] Reference DCG-ARTICLE-2008-010doi:10.2307/2323956 Record created on 2008-11-17, modified on 2017-05-12