3 problems

Determinant hom-counting conjecture. The following are equivalent:

Two-test hom-counting conjecture. The following are equivalent:

Let $k\ge 1$. Fix a set $\Gamma$ of colours and consider graphs $G$ whose colour interpretations satisfy $\operatorname{rg}(\gamma^G)\subseteq\Gamma$. For graphs $G,G'$ and a finit…