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

Ruixia Wang; Linxin Wu; Wei Meng

doi:10.46298/dmtcs.5851

Ruixia Wang ; Linxin Wu ; Wei Meng - Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs

dmtcs:5851 - Discrete Mathematics & Theoretical Computer Science, January 20, 2022, vol. 23:3 - https://doi.org/10.46298/dmtcs.5851

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

Authors: Ruixia Wang ; Linxin Wu ; Wei Meng

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.

Comment: 12 pages

https://doi.org/10.46298/dmtcs.5851

Source: arXiv.org:1910.05542

Volume: vol. 23:3

Section: Graph Theory

Published on: January 20, 2022

Accepted on: August 23, 2021

Submitted on: October 17, 2019

Keywords: Mathematics - Combinatorics, 05C20

Licence: arXiv.org - Non-exclusive license to distribute