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Discrete & Computational Geometry

, Volume 29, Issue 2, pp 223–227 | Cite as

A Euclidean Ramsey Problem

Abstract. Let C n denote the set of points in R n 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 C n contains a monochromatic plane K 4 . 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.

Keywords

Experimental Evidence Complete Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 2003

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

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