English

Are highly connected 1-planar graphs Hamiltonian?

Discrete Mathematics 2019-11-07 v1 Combinatorics

Abstract

It is well-known that every planar 4-connected graph has a Hamiltonian cycle. In this paper, we study the question whether every 1-planar 4-connected graph has a Hamiltonian cycle. We show that this is false in general, even for 5-connected graphs, but true if the graph has a 1-planar drawing where every region is a triangle.

Keywords

Cite

@article{arxiv.1911.02153,
  title  = {Are highly connected 1-planar graphs Hamiltonian?},
  author = {Therese Biedl},
  journal= {arXiv preprint arXiv:1911.02153},
  year   = {2019}
}
R2 v1 2026-06-23T12:06:54.970Z