A267295 Circulant Ramsey numbers RC_2(3,n) of the second kind.

3, 6, 9, 14, 17, 22, 27, 36, 39, 46, 49

Offset

2,1

Comments

The smallest number a(n), such that any triangle-free cyclic (also known as circulant) graph with at least a(n) vertices has independence number at least n. The terminology and the terms given here are from Harborth and Krause (2003); however, in another form, essentially they were considered and partly calculated already by Kalbfleich in 1965.

a(n) = A000789(n)+1 and a(n) >= A267296(n) for all n.

Moreover, the sequence is related to the ordinary two-color Ramsey numbers R(3,n), given in A000791, by the relation a(n) <= A000791(n) for all n, as proved by Kalbfleisch. This inequality is known to be strict for 6 <= n <= 8, and for n = 10.

References

H. Harborth, S. Krause: Ramsey Numbers for Circulant Colorings, Congressus Numerantium 161 (2003), 139-150.

Links

Table of n, a(n) for n=2..12.

J. G. Kalbfleisch, Construction of special edge-chromatic graphs, Canad. Math. Bull., 8 (1965), 575-584.

Index entries for sequences related to Ramsey numbers

Crossrefs

Cf. A000789, A000791, A267296.

Sequence in context: A310162 A310163 A310164 * A265321 A187263 A230876

Adjacent sequences: A267292 A267293 A267294 * A267296 A267297 A267298

Keyword

nonn,hard,more

Author

Jörgen Backelin, Jan 12 2016

Status

approved