English

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.

Keywords

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}
}
R2 v1 2026-07-01T08:22:11.960Z