Diameter three orientability of bipartite graphs
Summary: In [Discrete Math. 342, No. 4, 1063--1065 (2019; Zbl 1405.05044)], \textit{É. Czabarka} et al. showed that for every undirected graph of order \(n\), the minimum degree threshold for diameter two orientability is \(\frac{n}{2}+ \Theta(\ln n)\). In this paper, we consider bipartite graphs and give a sufficient condition in terms of the minimum degree for such graphs to have oriented diameter three. We in particular prove that for balanced bipartite graphs of order \(n\), the minimum degree threshold for diameter three orientability is \(\frac{n}{4}+\Theta(\ln n)\).
scientific article; zbMATH DE number 7356168
scientific article