4-connected 1-planar chordal graphs are Hamiltonian-connected
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914768376299520 |
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| author | Zhang, Licheng Huang, Yuanqiu Lv, Shengxiang Dong, Fengming |
| author_facet | Zhang, Licheng Huang, Yuanqiu Lv, Shengxiang Dong, Fengming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 4-connected 1-planar chordal graphs are Hamiltonian-connected Zhang, Licheng Huang, Yuanqiu Lv, Shengxiang Dong, Fengming Combinatorics 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. |
| title | 4-connected 1-planar chordal graphs are Hamiltonian-connected |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.15663 |