Euclidean ramsey theorems. I

P. Erdös, R. L. Graham, P. Montgomery, B. L. Rothschild, J. Spencer, E. G. Straus

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)341-363
Number of pages23
JournalJournal of Combinatorial Theory, Series A
Volume14
Issue number3
DOIs
StatePublished - May 1973

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Euclidean ramsey theorems. I'. Together they form a unique fingerprint.

  • 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