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arXiv · 2105.13040

On Morphing 1-Planar Drawings

Patrizio Angelini·Michael A. Bekos·Fabrizio Montecchiani·Maximilian Pfister
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Abstract

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of topology-preserving morphs for pairs of non-planar graph drawings. We make a step towards this problem by showing that a topology-preserving morph always exists for drawings of a meaningful family of $1$-planar graphs. While our proof is constructive, the vertices may follow trajectories of unbounded complexity.

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Patrizio Angelini, Michael A. Bekos, Fabrizio Montecchiani, Maximilian Pfister. 2021-05-27. On Morphing 1-Planar Drawings. https://arxiv.org/abs/2105.13040

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