  Regular edge-colored graphs encode colored triangulations of
pseudo-manifolds. Here we study families of edge-colored graphs built from a
finite but arbitrary set of building blocks, which extend the notion of
$p$-angulations to arbitrary dimensions. We prove the existence of a bijection
between any such family and some colored combinatorial maps which we call
stuffed Walsh maps. Those maps generalize Walsh's representation of hypermaps
as bipartite maps, by replacing the vertices which correspond to hyperedges
with non-properly-edge-colored maps. This shows the equivalence of tensor
models with multi-trace, multi-matrix models by extending the intermediate
field method perturbatively to any model. We further use the bijection to study
the graphs which maximize the number of faces at fixed number of vertices and
provide examples where the corresponding stuffed Walsh maps can be completely
characterized.
