On the decomposition of $n$-partite graphs based on a vertex-removing synchronised graph product

TL;DR

This paper introduces a new graph-decomposition theorem for acyclic n-partite multigraphs using a vertex-removing synchronised product, extending previous work on graph products motivated by real-time process synchronization.

Contribution

The paper presents a novel decomposition theorem based on VRSP for specific edge-labelled acyclic n-partite multigraphs, advancing graph theory in synchronization contexts.

Findings

Decomposition of acyclic n-partite multigraphs using VRSP.

Extension of graph-decomposition theorems with applications in real-time processes.

Relation of VRSP to known graph products like Cartesian and synchronised products.

Abstract

Recently, we have introduced and modified graph-decomposition theorems based on a 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 W\"ohrle and Thomas. Here, we introduce a new graph-decomposition theorem based on the VRSP that decomposes an edge-labelled acyclic n-partite multigraph where all labels are the same.