标题： 在一般位置下穿过笛卡尔积、冠图和联结 显示英文标题

标题： Moving through Cartesian products, coronas and joins in general position

摘要： 广义位置问题要求找到较大的顶点集合，使得该集合中没有三个顶点位于同一条最短路径上。最近，这个问题被定义了一个动态版本，称为\emph{移动一般位置问题}，在这个问题中，一组机器人必须访问图中的所有顶点，同时保持广义位置。本文研究了笛卡尔积、冠积和联结在广义位置问题中的情况，给出了通用图的上下界，并得出了包括网格、圆柱、哈明图和树棱柱在内的图族的确切值。 显示英文摘要

摘要： The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was defined, called the \emph{mobile general position problem}, in which a collection of robots must visit all the vertices of the graph whilst remaining in general position. In this paper we investigate this problem in the context of Cartesian products, corona products and joins, giving upper and lower bounds for general graphs and exact values for families including grids, cylinders, Hamming graphs and prisms of trees.