|
|
COMMENTS
|
A Ramsey-like number but defined for tournaments (i.e., directed graphs in which each node-pair is joined by exactly one arc) rather than undirected graphs.
It is not hard to show that a(n) always exists and a(n) is nondecreasing.
The lower bounds a(4)>=8 and a(5)>=14 and a(6)>=28 arise from the cyclic tournaments with offsets 1,2,4 mod 7; the same is true of offsets 1,3,9,2,6,5 mod 13 and the "QRgraph" in GF(3^3) with 27 vertices.
The following lower bounds a(n)>=P+1 arise from QRgraph(P) where P is prime and P=3 (mod 4): a(8)>=48, a(9)>=84, a(10)>=108, a(12)>=200, a(13)>=272.
This is almost certainly different from the other sequences currently in the OEIS which begin 1,2,4,8,14,28.
|
