A389335 - OEIS

A389335

a(n) is the smallest m such that for every red-green-blue edge-coloring of the graph K_{m} there exists at least one red, green or blue n-cycle; Ramsey number r(C_n, C_n, C_n).

17, 11, 17, 12, 25, 16

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OFFSET

3,1

LINKS

Table of n, a(n) for n=3..8.

Fabricio Siqueira Benevides and Jozef Skokan, The 3-colored Ramsey number of even cycles, J. Combin. Theory Ser. B (2009), 690-708.

Thomas Bloom, Problem 556, Erdős Problems.

J. A. Bondy and P. Erdős, Ramsey numbers for cycles in graphs, J. Combin. Theory Ser. B 14 (1973), 46-54.

Yoshiharu Kohayakawa, Miklós Simonovits, and Jozef Skokan, The 3-colored Ramsey number of odd cycles, Electronic Notes in Discrete Mathematics, Volume 19, 2005, Pages 397-402, Proceedings of GRACO2005, 397-402.

Tomasz Łuczak, R(C_n,C_n,C_n) < (4+o(1))n. J. Combin. Theory Ser. B (1999), 174-187.

Stanisław Radziszowski, Small Ramsey Numbers, Electronic J. Comb., DS1.

FORMULA

A conjecture by Bondy and Erdős: a(n) <= 4n - 3 for n >= 4.

a(n) = (4 + o(1))n for odd n (Łuczak).

a(n) <= 3n + o(n) for even n (Łuczak).

a(n) = 4n - 3 for sufficiently large odd n (Kohayakawa, Simonovits, and Skokan).

a(n) = 2n for sufficiently large even n (Benevides and Skokan).

CROSSREFS

Cf. A389334 (3 color Ramsey numbers for unequal cycles).

Cf. A389313, A389310 (two color Ramsey numbers for cycles).

Sequence in context: A166524 A106791 A040274 * A164064 A369490 A279232