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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

All triangles are Ramsey


Authors: Peter Frankl and Vojtěch Rödl
Journal: Trans. Amer. Math. Soc. 297 (1986), 777-779
MSC: Primary 05A99; Secondary 51M99
DOI: https://doi.org/10.1090/S0002-9947-1986-0854099-6
MathSciNet review: 854099
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a triangle $ ABC$ and an integer $ r$, $ r \geqslant 2$, it is shown that for $ n$ sufficiently large and an arbitrary $ r$-coloring of $ {R^n}$ one can find a monochromatic copy of $ ABC$.


References [Enhancements On Off] (What's this?)

  • [1] P. Erdös, R. L. Graham, P. Montgomery, B. L. Rothschild, J. H. Spencer and E. G. Straus, Euclidean Ramsey theorems, J. Combin. Theory Ser. A 14 (1973), 341-363. MR 0316277 (47:4825)
  • [2] F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264-286.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0854099-6
Article copyright: © Copyright 1986 American Mathematical Society

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