2 problems

Incoherence conjecture for forests. The ideal $\mathcal I$ is incoherent if and only if $H$ is a forest.

Sparse Erdős–Hajnal conjecture. For every proper ideal $\mathcal I$ there exist $\epsilon>0$ and $c>0$ such that every $\epsilon$-coherent graph $G\in\mathcal I$ satisfies