On the existence and number of $(k+1)$-kings in $k$-quasi-transitive digraphs

Hortensia Galeana-Sánchez, César Hernández-Cruz, Manuel Alejandro Juárez-Camacho

Let $D=(V(D),A(D))$ be a digraph and $k\ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0,v_1,...,v_k)$ in $D$, then $(v_0, v_k) \in A(…