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

Deleting edges to restrict the size of an epidemic in temporal networks