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arXiv · 1911.02153

Are highly connected 1-planar graphs Hamiltonian?

Therese Biedl
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Abstract

It is well-known that every planar 4-connected graph has a Hamiltonian cycle. In this paper, we study the question whether every 1-planar 4-connected graph has a Hamiltonian cycle. We show that this is false in general, even for 5-connected graphs, but true if the graph has a 1-planar drawing where every region is a triangle.

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Therese Biedl. 2019-11-06. Are highly connected 1-planar graphs Hamiltonian?. https://arxiv.org/abs/1911.02153

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