Summary: The mesh of trees network supports many simple parallel algorithms. These algorithms can all be immediately translated to the hypercube by a known efficient embedding of the mesh of trees into the hypercube. However, no such embeddings have been found into any of the bounded-degree variants of the hypercube, thus restricting this class of networks’ ability to simulate mesh of trees algorithms. In this paper we demonstrate an efficient embedding of the mesh of trees into the de Bruijn graph, allowing this network (and the closely related shuffle-exchange graph) to simulate arbitrary mesh of trees computations. This result also widens the class of mesh of trees computations that can be simulated by the butterfly and its related networks, though to a lesser degree.