  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 modeled 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.
