R   I T   D-p A  G T

Studying parallelism and concurrency in the double-pushout approach to graph transformations is mainly based on the so-called triple-pushout condition. The categories of sets and of graphs satisfy this condition. If we, however, consider graph morphisms that may change the labels in a welldefined manner (structurally labeled graphs), the triple-pushout condition does no longer hold true. In this paper, we propose a restriction on the structure of the alphabet such that on the one hand, the triple-pushout condition can be proved, and on the other hand, relevant applications are covered, e.g., term graph rewriting.