4‐Connected 1‐Planar Chordal Graphs Are Hamiltonian‐Connected
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.
Authors
- Fengming Dong (ORCID: https://orcid.org/0000-0002-8510-2262)
- Yuanqiu Huang (ORCID: https://orcid.org/0000-0002-6081-6293)
- Shengxiang Lv (ORCID: https://orcid.org/0000-0001-8826-7890)
- Licheng Zhang (ORCID: https://orcid.org/0000-0002-9164-1289)
Institutions
- Hunan University (CN)
- Nanyang Technological University (SG)
- Hunan Normal University (CN)
- Changsha Normal University (CN)
- Hunan University of Finance and Economics (CN)
Publication Details
- Journal
- Journal of Graph Theory
- Published
- 2025-04-18
- DOI
- https://doi.org/10.1002/jgt.23250
- Primary Topic
- Advanced Graph Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00