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arXiv · 2607.25553

On the $2$-Bend Slope Number of $1$-Planar Graphs

Michael A. Bekos·Eleni Katsanou·Philipp Kindermann·Aikaterini Maria Ntasiou·Maria Eleni Pavlidi·Soeren Terziadis
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Abstract

While drawing planar graphs with few slopes and few bends is a well-studied problem, corresponding extensions to beyond-planar graphs still remain mostly unexplored. Motivated by this observation, in this work, we provide bounds on the slope number of biconnected $1$-planar graphs when two bends are allowed along each edge. Our contribution is an incremental drawing algorithm that produces $2$-bend $1$-planar drawings of biconnected $1$-plane graphs with maximum degree $\Delta$ using any prescribed set of $\Delta$ pairwise distinct slopes.

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Michael A. Bekos, Eleni Katsanou, Philipp Kindermann, Aikaterini Maria Ntasiou, Maria Eleni Pavlidi, Soeren Terziadis. 2026-07-28. On the $2$-Bend Slope Number of $1$-Planar Graphs. https://arxiv.org/abs/2607.25553

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