Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs

Abstract

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 $uv\notin A(D)$ and $vu\notin A(D)$. 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 $d(u)+d(v)\ge 3a-1$ whenever $uv\notin A(D)$ and $vu\notin A(D)$, then $D$ is traceable. The lower bound $3a-1$ is tight.

12 pages

References in corpus (1)

• A sufficient condition for a balanced bipartite digraph to be hamiltonian

Cited by in corpus (1)

• A new sufficient condition for a 2-strong digraph to be Hamiltonian