Data exchange is the problem of translating data structured under a source schema according to a target schema and a set of source-to-target constraints known as schema mappings. In this paper, we investigate the problem of data exchange in a heterogeneous setting, where the source is a relational database, the target is a graph database, and the schema mappings are defined across them. We study the classical problems considered in data exchange, namely the existence of solutions and query answering. We show that both problems are intractable in the presence of target constraints, already under significant restrictions.