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On the oriented diameter of near planar triangulations

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arxiv 2312.03258 v1 pith:2SFQYENC submitted 2023-12-06 math.CO

Yiwei Ge , Xiaonan Liu , Zhiyu Wang This is my paper · ORCID
classification math.CO
keywords diameterorientedboundnearplanartriangulationsupperconnected
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abstract

In this paper, we show that the oriented diameter of any $n$-vertex $2$-connected near triangulation is at most $\lceil{\frac{n}{2}}\rceil$ (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 $n/2+O(\sqrt{n})$ on the oriented diameter of planar triangulations by Mondal, Parthiban and Rajasingh.

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