2 problems

Bang-Jensen and Wang's conjecture. Every $2$-arc-strong semicomplete split digraph $D$ contains a good $(u,v)$-pair for every choice of vertices $u,v$ in $D$.

Bounded-independent-set conjecture. For every fixed integer $k$, the Hamiltonian-cycle problem is polynomial-time solvable for the class of split digraphs $D=(V_1,V_2;A)$ in which…