- Abstract. We introduce a notion of equally constrained variables of a constraint network. We propose a method of pruning that uses the notion. We combine the proposed method of pruning with FC-CBJ and call the resulting algorithm FC-CBJ-EQ. Our experimental results show that FC-CBJ-EQ outperforms FC-CBJ on constraint networks that encode randomly generated instances of graph k-coloring and of the subgraph isomorphism problems.