Metric space method for constructing splitting partitions of graphs

In an earlier work [6] the concept of splitting partition of a graph was introduced in connection with the maximum clique problem. A splitting partition of a graph can be used to replace the graph by two smaller graphs in the course of a clique search algorithm. In other words splitting partitions can serve as a branching rule in an algorithm to compute the clique number of a given graph. In the paper we revisit this branching idea. We will describe a technique to construct not necessary optimal splitting partitions. The given graph can be viewed as a metric space and the geometry of this space plays a guiding role. In order to assess the performance of the procedure we carried out numerical experiments.