Cartesian products of graphs as subgraphs of de Bruijn graphs of dimension at least three

Given a Cartesian product G = G 1 \Theta : : : \Theta Gm (m 2) of nontrivial connected graphs G i and the base d, dimension D de Bruijn graph B(d; D), it is investigated under which conditions G is (or is not) a subgraph of B(d; D). We present a complete solution of this problem for the case D 4. For D = 3, we give partial results including a complete solution for the case that G is a torus, i.e., G is the Cartesian product of cycles