Geodesic
Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs
Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3.

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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 $d(u)+d(v)\geq 3a-1$ whenever $uv\notin A(D)$ and $vu\notin A(D)$, then $D$ is traceable. The lower bound $3a-1$ is tight.
DOI : 10.46298/dmtcs.5851
Classification : 05C20, 05C35, 05C45 
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     title = {Extremal digraphs on {Meyniel-type} condition for hamiltonian cycles in balanced bipartite digraphs},
     journal = {Discrete mathematics & theoretical computer science},
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Wang, Ruixia; Wu, Linxin; Meng, Wei. Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs. Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3. doi : 10.46298/dmtcs.5851. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.5851/

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