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A000791 Ramsey numbers R(3,n).
(Formerly M2530 N0998)
8
1, 3, 6, 9, 14, 18, 23, 28, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(10) is either 40, 41, or 42 (Goedgebeur, Radziszowski). - Ray G. Opao, Oct 07 2015
Kim proves that a(n) ≍ n/log n; the lower and upper constants, respectively, can be chosen arbitrarily close to 1/162 and 1. (Kim notes that he made no attempt to make 1/162 tight.) - Charles R Greathouse IV, Jun 23 2023
REFERENCES
G. Berman and K. D. Fryer, Introduction to Combinatorics. Academic Press, NY, 1972, p. 175.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 288.
J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 840.
Brendan McKay, personal communication.
H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 42.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vigleik Angeltveit, R(3,10) <= 41, arXiv:2401.00392 [math.CO], 2023.
J. Goedgebeur and S. Radziszowski, New Computational Upper Bounds for Ramsey Numbers R(3,k), arXiv:1210.5826 [math.CO], 2012-2013.
R. E. Greenwood and A. M. Gleason, Combinatorial relations and chromatic graphs, Canad. J. Math., 7 (1955), 1-7.
J. G. Kalbfleisch, Construction of special edge-chromatic graphs, Canad. Math. Bull., 8 (1965), 575-584.
Jeong Han Kim, The Ramsey number R(3, t) has order of magnitude t^2/log t, Random Structures & Algorithms Vol. 7, No. 3 (1995), pp. 173-207.
Richard L. Kramer, Ricardo's Ramsey Number Page
Math Reference Project, Ramsey Numbers
Mathematical Database, Ramsey's Theory
Online Dictionary of Combinatorics, Ramsey's Theorem
I. Peterson, Math Trek, Party Games, Science News Online, Vol. 156, No. 23, Dec 04 1999.
I. Peterson, Math Trek, Party Games, Dec 06 1999.
Stanislaw Radziszowski, Small Ramsey Numbers, The Electronic Journal of Combinatorics, Dynamic Surveys, #DS1: Jan 12, 2014.
Eric Weisstein's World of Mathematics, Ramsey Number
Wikipedia, Ramsey's Theorem.
Jin Xu and C. K. Wong, Self-complementary graphs and Ramsey numbers I, Discrete Math., 223 (2000), 309-326.
CROSSREFS
A row of the table in A059442. Cf. A120414.
Sequence in context: A265321 A187263 A230876 * A027424 A294476 A258087
KEYWORD
nonn,hard,more,nice
AUTHOR
EXTENSIONS
a(1) = 1 added by N. J. A. Sloane, Nov 05 2023
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)