2 problems

Chen's conjecture. There do not exist any $(G,3)$-arc-transitive, $G$-vertex-primitive digraphs with $G$ almost simple.

Let $\Gamma$ be a vertex-primitive $s$-arc-transitive digraph, and let $s$ denote its arc-transitivity parameter. Exclude directed cycles. Conjecture. The upper bound on $s$ for al…