Note on decompositions based on the vertexremoving synchronised graph product

Recently, we have introduced two graph-decomposition theorems based on a new graph product,
motivated by applications in the context of synchronising periodic real-time processes. This vertexremoving synchronised product (VRSP) is based on modifications of the well-known Cartesian
product and is closely related to the synchronised product due to Wohrle and Thomas. Here, we ¨
show how we can relax the requirements of these two graph-decomposition theorems.