login
Circulant Ramsey numbers RC_2(3,n) of the second kind.
1

%I #18 Sep 14 2019 06:38:34

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

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

%C 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.

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

%C 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.

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

%H J. G. Kalbfleisch, <a href="http://dx.doi.org/10.4153/CMB-1965-041-7">Construction of special edge-chromatic graphs</a>, Canad. Math. Bull., 8 (1965), 575-584.

%H <a href="/index/Ra#Ramsey numbers">Index entries for sequences related to Ramsey numbers</a>

%Y Cf. A000789, A000791, A267296.

%K nonn,hard,more

%O 2,1

%A _Jörgen Backelin_, Jan 12 2016