Euclidean ramsey theorems. I

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

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - May 1973

ASJC Scopus subject areas

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


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