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arXiv · 2610.05061

An asymptotically tight bound on oriented diameter

Yaojun Chen·Jifu Lin·Xiaolin Wang·Ruilin Zheng
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Abstract

Let $f(d)$ be the smallest integer such that every connected bridgeless graph of diameter $d$ admits an orientation with directed diameter at most $f(d)$. Chvátal and Thomassen (1978) proved $\left\lceil{d^2}/{2}\right\rceil+d\le f(d) \le 2d^2+2d$. In this paper, we prove that $f(d)\le \left\lceil d^2/2\right\rceil+6d$, which shows $f(d)= d^2/2+Θ(d)$ and determine the leading quadratic coefficient of $f(d)$. The key method of our proof is to construct a central subgraph $H$ such that it admits a strong orientation of diameter $O(d)$ and the distance between $H$ and every vertex outside $H$ is at most $ d/2 $.

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Yaojun Chen, Jifu Lin, Xiaolin Wang, Ruilin Zheng. 2026-10-04. An asymptotically tight bound on oriented diameter. https://arxiv.org/abs/2610.05061

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