The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families -- intersection graphs of Jordan regions, unit contact disk graphs (penny graphs), and chordal graphs. For each of these graph families, we present space-efficient algorithms for the Reachability problem. In order to obtain these results, we use the vertex separator of these graphs effectively, and design space-efficient algorithms to find such separators. The constructions of the separators presented here can be of independent interest.

中文翻译：

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几何图中可达性的空间有效算法

图可达性的问题是确定给定图中是否存在从一个顶点到另一个顶点的路径。在本文中，我们研究了三个不同的图族的可达性问题-Jordan区域的相交图，单位接触盘图（便士图）和弦图。对于这些图族中的每一个，我们都针对可到达性问题提出了节省空间的算法。为了获得这些结果，我们有效地使用了这些图的顶点分隔符，并设计了节省空间的算法来查找此类分隔符。此处介绍的分隔器的结构可能是独立引起关注的。