Discrete & Computational Geometry

, Volume 29, Issue 2, pp 223–227

A Euclidean Ramsey Problem

DOI: 10.1007/s00454-002-0780-5

Cite this article as:
Exoo Discrete Comput Geom (2003) 29: 223. doi:10.1007/s00454-002-0780-5

Abstract. Let Cn denote the set of points in Rn whose coordinates are all 0 or 1 , i.e., the vertex set of the unit n -cube. Graham and Rothschild [2] proved that there exists an integer N such that for n ≥ N , any 2-coloring of the edges of the complete graph on Cn contains a monochromatic plane K4 . Let N* be the minimum such N . They noted that N* must be at least 6 . Their upper bound on N* has come to be known as Graham's number , often cited as the largest number that has ever been put to any practical use. In this note we show that N* must be at least 11 and provide some experimental evidence suggesting that N* is larger still.

Copyright information

© 2002 Springer-Verlag New York Inc.

Authors and Affiliations

  •  Exoo
    • 1
  1. 1.Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA g-exoo@indstate.eduUS