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arXiv · 2608.19089

Improved bounds on the oriented diameter of planar triangulations

Xiaonan Liu
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Abstract

The oriented diameter of a connected bridgeless graph $G$, denoted by $\overrightarrow{\operatorname{diam}}(G)$, is the minimum diameter among all strong orientations of $G$. We study the oriented diameter of planar triangulations, and show that $\overrightarrow{\operatorname{diam}}(G)\leq \frac{2n+44}{5}$ for any $n$-vertex planar triangulation $G$. This improves the leading constant in the previous best general upper bound $\lceil \frac{n}{2}\rceil$, due to Ge, Liu, and Wang, from $1/2$ to $2/5$. We also prove that every $n$-vertex $4$-connected planar triangulation satisfies $\overrightarrow{\operatorname{diam}}(G)\leq \frac{n+17}{3}$.

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Xiaonan Liu. 2026-08-19. Improved bounds on the oriented diameter of planar triangulations. https://arxiv.org/abs/2608.19089

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