For s >= 4, the 3-uniform tight cycle C3 s has vertex set corresponding to s distinct points on a circle and edge set given by the s cyclic intervals of three consecutive points. For fixed s >= 4 and s ≡ 0 (mod 3), we prove that there are positive constants a and b with 2at < r(C3 s,K3 t ) < 2bt2 log t. The lower bound is obtained via a probabilistic construction. The upper bound for s …