The smallest number of vertices in a 2-arc-strong digraph which has no
good pair
The smallest number of vertices in a 2-arc-strong digraph which has no
good pair
Bang-Jensen, Bessy, Havet and Yeo showed that every digraph of independence number at most 2 and arc-connectivity at least 2 has an out-branching $B^+$ and an in-branching $B^-$ which are arc-disjoint (such two branchings are called a {\it good pair}), which settled a conjecture of Thomassen for digraphs of independence …