Erdős-Hajnal bound for the three-edge hypergraph on four vertices
= Erdős-Hajnal bound for the three-edge hypergraph on four vertices
{c}
Let $K_4^{(3)-}$ be the three-uniform hypergraph with three of the four possible edges on four vertices. Every $K_4^{(3)-}$-free three-uniform hypergraph on $N$ vertices has an independent set of size at least
$$
c\frac{\log N}{\log\log N}.
$$
Equivalently, $r(K_4^{(3)-},K_k^{(3)})\leq k^{Ck}$.