Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs
Ruixia Wang, Linxin Wu, Meng Wei · Discrete Mathematics & Theoretical Computer Science · 2022
Let $D$ be a strong balanced digraph on $2a$ vertices. Adamus et al. have proved that $D$ is hamiltonian if $d(u)+d(v)\ge 3a$ whenever $uv otin A(D)$ and $vu otin A(D)$. The lower bound $3a$ is tight. In this paper, we shall show that the extremal digraph on this condition is two classes of digraphs that can be clearly characterized. Moreover, we also show that if $d(u)+d(v)\geq 3a-1$ whenever $uv otin A(D)$ and $vu otin A(D)$, then $D$ is traceable. The lower bound $3a-1$ is tight.