# The edge labeling of higher order Voronoi diagrams

@article{Claverol2021TheEL, title={The edge labeling of higher order Voronoi diagrams}, author={Merc{\`e} Claverol and Andrea de las Heras Parrilla and Clemens Huemer and Alejandra Mart'inez-Moraian}, journal={ArXiv}, year={2021}, volume={abs/2109.13002} }

We present an edge labeling of order-k Voronoi diagrams, Vk(S), of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that Vk(S) has a small orientable cycle and path double cover, and we identify configurations that cannot appear in Vk(S) for small values of k. This paper also contains a systematic study of well-known and new properties of Vk(S), all whose proofs only rely on elementary geometric arguments in the plane. The maybe most…

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