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A003323 Multicolor Ramsey numbers R(3,3,...,3), where there are n 3's.
(Formerly M2594)
3, 6, 17, 62, 327 (list; graph; refs; listen; history; text; internal format)



Definition: if the edges of a complete graph with at least a(n) nodes are colored with n colors then there is always a monochromatic triangle, and a(n) is the smallest number with this property.

Has it been proved that a(4)=62, or is it just an upper bound? - N. J. A. Sloane, Jun 12 2016

62 is an upper bound.  It is probably not the correct value, which is likely closer to the lower bound of 51. - Jeremy F. Alm, Jun 12 2016


G. Berman and K. D. Fryer, Introduction to Combinatorics. Academic Press, NY, 1972, p. 175.

S. Fettes, R. Kramer, S. Radziszowski, An upper bound of 62 on the classical Ramsey number R(3,3,3,3), Ars Combin. 72 (2004), 41-63.

H. W. Gould, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..5.

R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math., 7 (1955), 1-7.

H. W. Gould, Letters to N. J. A. Sloane, 1974


a(2)=6 since in a party with at least 6 people, there are three people mutually acquainted or three people mutually unacquainted.


Cf. A045652.

A073591(n) is an upper bound on a(n).

Sequence in context: A287901 A143093 A117712 * A106158 A274103 A195995

Adjacent sequences:  A003320 A003321 A003322 * A003324 A003325 A003326




N. J. A. Sloane.


Upper bound and additional comments from D. G. Rogers, Aug 27 2006

Better definition from Max Alekseyev, Jan 12 2008

Comment corrected by Brian Kell, Feb 14 2010

Changed a(4) to 62, following Fettes et al. - Jeremy F. Alm, Jun 08 2016

Entry revised by N. J. A. Sloane, Jun 12 2016



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Last modified March 1 03:09 EST 2021. Contains 341732 sequences. (Running on oeis4.)