Year: 2026
Type: preprint
Abstract: The oriented diameter of a connected bridgeless graph is the minimum diameter of a strong orientation. Let $f(d)$ be the maximum oriented diameter among all such graphs of diameter $d$. In 1978, Chvátal and Thomassen proved $f(d)\le2d^2+2d$ and constructed graphs showing that any quadratic upper bound on $f(d)$ must have leading coefficient at least $1/2$. We prove that $f(d)\le \tfrac12d^2+7d$ for every integer $d\ge1$. This matches the leading coefficient of their lower bound and establishes $f(d)=\tfrac12d^2+O(d)$, determining the optimal quadratic coefficient. Our proof gives a polynomial-time algorithm that constructs a strong orientation satisfying the stated bound.
Source: arXiv (Cornell University)
Authors: Ai, Jiangdong, Feng, Yaokun, Lei, Hui, Ren, Zijian
Institutions: Nankai University, Hong Kong Polytechnic University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220739001