标题： 通过笛卡尔积、冠和并集在一般位置中的移动 显示英文标题

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

摘要： 一般位置问题要求找到大的顶点集合，使得该集合中的任何三个顶点都不位于同一条最短路径上。 最近定义了该问题的一个动态版本，称为\emph{移动通用位置问题}，其中一组机器人必须访问图的所有顶点，同时保持在一般位置。 在本文中，我们研究了该问题在笛卡尔积、冠积和联积中的情况，给出了一般图的上下界，并给出了包括网格、圆柱体、哈明图和树的棱柱在内的族的精确值。 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.