### Abstract

The general Ramsey problem can be described as follows: Let A and B be two sets, and R a subset of A × B. For a ε{lunate} A denote by R(a) the set {b ε{lunate} B | (a, b) ε{lunate} R}. R is called r-Ramsey if for any r-part partition of B there is some a ε{lunate} A with R(a) in one part. We investigate questions of whether or not certain R are r-Ramsey where B is a Euclidean space and R is defined geometrically.

Original language | English (US) |
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Pages (from-to) | 341-363 |

Number of pages | 23 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - May 1973 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Erdös, P., Graham, R. L., Montgomery, P., Rothschild, B. L., Spencer, J., & Straus, E. G. (1973). Euclidean ramsey theorems. I.

*Journal of Combinatorial Theory, Series A*,*14*(3), 341-363. https://doi.org/10.1016/0097-3165(73)90011-3