Networked control problems of multi-agent systems can be distributed to the agents to reduce computational effort. One distribution strategy is priority-based non-cooperative distributed model predictive control (P-DMPC), in which the computation time is mainly determined by the longest path in the coupling directed acyclic graph (DAG). The longest path is dependent on the undirected coupling graph, which is fixed, and the priority assignment, which is variable. This article presents an approach to assign priorities in P-DMPC to reduce the longest path length in the coupling DAG and therefore the computation time for the networked control system (NCS). We proof that this problem can be mapped to a graph-coloring problem, in which the number of needed colors corresponds to the longest path length in the coupling DAG. We present an efficient graph-coloring algorithm from which we determine priorities for the agents. We evaluate effect and effort of the approach before applying it to trajectory planning for networked vehicles at intersections.