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arXiv · 2404.15663

4-connected 1-planar chordal graphs are Hamiltonian-connected

Licheng Zhang·Yuanqiu Huang·Shengxiang Lv·Fengming Dong
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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.

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Licheng Zhang, Yuanqiu Huang, Shengxiang Lv, Fengming Dong. 2024-04-24. 4-connected 1-planar chordal graphs are Hamiltonian-connected. https://arxiv.org/abs/2404.15663

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