5 problems

Borel Almost Finiteness Conjecture. Every uniformly Borel amenable Følner graph is Borel almost finite.

Let $X$ be the space of vertices in the setting of Theorem 6.1, and let $G$ be the corresponding locally countable $F_\sigma$ graph. Compactness conjecture. The compactness of $X$…

Let $G$ be a Borel graph with Borel chromatic number $4\chi_B(G)=\Delta(G)+14$, where $\Delta(G)$ denotes the maximum degree of $G$. A Borel homomorphic copy of the corresponding e…

Borel chromatic-number conjecture.

Aperiodic Borel equitable Brooks conjecture. The graph $G$ has a $\mu$-equitable $\Delta$-coloring.