English

4-connected 1-planar chordal graphs are Hamiltonian-connected

Combinatorics 2024-04-25 v1

Abstract

Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar chordal graphs, and show that all such graphs are Hamiltonian-connected. A crucial tool used in our proof is a characteristic of 1-planar 4-trees.

Keywords

Cite

@article{arxiv.2404.15663,
  title  = {4-connected 1-planar chordal graphs are Hamiltonian-connected},
  author = {Licheng Zhang and Yuanqiu Huang and Shengxiang Lv and Fengming Dong},
  journal= {arXiv preprint arXiv:2404.15663},
  year   = {2024}
}