Note on decompositions based on the vertex removing 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 vertex removing 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.