All triangles are Ramsey
HTML articles powered by AMS MathViewer
- by Peter Frankl and Vojtěch Rödl PDF
- Trans. Amer. Math. Soc. 297 (1986), 777-779 Request permission
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
- P. Erdős, R. L. Graham, P. Montgomery, B. L. Rothschild, J. Spencer, and E. G. Straus, Euclidean Ramsey theorems. I, J. Combinatorial Theory Ser. A 14 (1973), 341–363. MR 316277, DOI 10.1016/0097-3165(73)90011-3 F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264-286.
Additional Information
- © Copyright 1986 American Mathematical Society
- 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