English

Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs

Combinatorics 2024-11-05 v2

Abstract

The existence of Hamiltonian cycles in 1-planar graphs with higher connectivity has attracted considerable attention. Recently, the authors and Dong proved that 4-connected 1-planar chordal graphs are Hamiltonian-connected. In this paper, we investigate the non-Hamiltonicity of a broader class of graphs, specifically perfect graphs, under the constraint of 1-planarity, with a focus on connectivity of at most 5. We also propose some unsolved problems.

Keywords

Cite

@article{arxiv.2410.22021,
  title  = {Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs},
  author = {Licheng Zhang and Shengxiang Lv and Yuanqiu Huang},
  journal= {arXiv preprint arXiv:2410.22021},
  year   = {2024}
}

Comments

8 pages, 2 figures