  We investigate the computational complexity of finding temporally disjoint
paths or walks in temporal graphs. There, the edge set changes over discrete
time steps and a temporal path (resp. walk) uses edges that appear at
monotonically increasing time steps. Two paths (or walks) are temporally
disjoint if they never use the same vertex at the same time; otherwise, they
interfere. This reflects applications in robotics, traffic routing, or finding
safe pathways in dynamically changing networks. On the one extreme, we show
that on general graphs the problem is computationally hard. The "walk version"
is W[1]-hard when parameterized by the number of routes. However, it is
polynomial-time solvable for any constant number of walks. The "path version"
remains NP-hard even if we want to find only two temporally disjoint paths. On
the other extreme, restricting the input temporal graph to have a path as
underlying graph, quite counterintuitively, we find NP-hardness in general but
also identify natural tractable cases.
