  We introduce the notion of strongly $\binom{k}{2}$-free graphs, which contain
dp-minimal graphs. We show that under some sparsity assumption, given a rainbow
$\binom{k}{2}$-free blockade we can find a rainbow $\binom{k-1}{2}$-free
blockade. This might serve as an intermediate step towards Erd\H os-Hajnal
property for dp-minimal graphs.
