We study unit disk visibility graphs, where the visibility relation between a pair of geometric entities is defined by not only obstacles, but also the distance between them. That is, two entities are not mutually visible if they are too far apart, regardless of having an obstacle between them. This particular graph class models real world scenarios more accurately compared to the conventional visibility graphs. We first define and classify the unit disk visibility graphs, and then show that the 3-coloring problem is NP-complete when unit disk visibility model is used for a set of line segments (which applies to a set of points) and for a polygon with holes.

中文翻译：

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单位磁盘可见性图

我们研究单位磁盘可见性图，其中一对几何实体之间的可见性关系不仅由障碍物定义，而且还由它们之间的距离定义。也就是说，如果两个实体相距太远，则彼此之间不可见，无论它们之间是否有障碍。与传统的可见性图相比，这种特殊的图类可以更准确地模拟现实世界的场景。我们首先定义和分类单位磁盘可见性图，然后证明当单位磁盘可见性模型用于一组线段（适用于一组点）和多边形时，三色问题是NP完全的有孔。