Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these processes spread are dynamic in nature, and can be modelled with temporal graphs. Here, we study the problem of deleting edges from a given temporal graph in order to reduce the number of vertices (temporally) reachable from a given starting point. This could be used to control the spread of a disease, rumour, etc. in a temporal graph. In particular, our aim is to find a temporal subgraph in which a process starting at any single vertex can be transferred to only a limited number of other vertices using a temporally-feasible path. We introduce a natural edge-deletion problem for temporal graphs and provide positive and negative results on its computational complexity and approximability.

图形上的传播过程是多种现实世界现象的自然模型，包括通过社交网络传播的信息和通过接触网络传播的生物疾病。通常，这些过程所散布的网络本质上是动态的，并且可以使用时间图进行建模。在这里，我们研究从给定的时间图中删除边的问题，以减少从给定的起点（临时）可到达的顶点数量。这可以用于在时间图中控制疾病，谣言等的传播。特别地，我们的目标是找到一个时间子图，其中可以使用时间上可行的路径将始于任何单个顶点的过程仅转移到有限数量的其他顶点。