A note on optimal 2-planar graphs
Combinatorics
2026-05-05 v3
Abstract
In this note, we prove that every 4-connected optimal 2-planar graph is Hamiltonian-connected. Furthermore, we show that the 4-connectedness condition is sharp by constructing infinitely many 3-connected optimal 2-planar graphs that are non-Hamiltonian.
Cite
@article{arxiv.2512.11535,
title = {A note on optimal 2-planar graphs},
author = {Licheng Zhang and Yuanqiu Huang and Zhangdong Ouyang},
journal= {arXiv preprint arXiv:2512.11535},
year = {2026}
}