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.
Recently, we have introduced and modified 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 recall the definition of the VRSP and the two modified graph-decompositions and introduce three new graph-decomposition theorems. The first new theorem decomposes a graph with respect to the semicomplete bipartite subgraphs of the graph. For the second new theorem, we introduce a matrix graph, which is used to decompose a graph in a manner similar to the decomposition of graphs using the Cartesian product. In the third new theorem, we combine these two types of decomposition. Ultimately, the goal of these graph-decomposition theorems is to come to a prime-graph decomposition.
MULTIFILE
Recently, we have introduced 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 closely related to the synchronised product due to Wöhrle and Thomas. Here, we recall the definition of the VRSP and use it to define two different decompositions of graphs. Although our main results apply to directed labelled acyclic multigraphs, the VRSP can also be used to decompose any undirected graph of order at least 4 into two smaller graphs.
