Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915002477182976 |
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| author | Zhang, Licheng Lv, Shengxiang Huang, Yuanqiu |
| author_facet | Zhang, Licheng Lv, Shengxiang Huang, Yuanqiu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs Zhang, Licheng Lv, Shengxiang Huang, Yuanqiu Combinatorics 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. |
| title | Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.22021 |