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arXiv · 2410.22021

Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs

Licheng Zhang·Shengxiang Lv·Yuanqiu Huang
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Abstract

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.

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Licheng Zhang, Shengxiang Lv, Yuanqiu Huang. 2024-11-03. Two classes of connectivity-related non-Hamiltonian 1-planar perfect graphs. https://arxiv.org/abs/2410.22021

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