In this paper, we show that the oriented diameter of any n-vertex 2-connected near triangulation is at most ⌈2n⌉ (except for seven small exceptions), and the upper bound is tight. This extends a result of Wang et.al. on the oriented diameter of maximal outerplanar graphs, and improves an upper bound of n/2+O(n) on the oriented diameter of planar triangulations by Mondal, Parthiban and Rajasingh.
@article{arxiv.2312.03258,
title = {On the oriented diameter of near planar triangulations},
author = {Yiwei Ge and Xiaonan Liu and Zhiyu Wang},
journal= {arXiv preprint arXiv:2312.03258},
year = {2023}
}