In the present paper we aim at speeding up the computation of exact graph edit distance. We propose to combine the standard tree search approach to graph edit distance computation with the suboptimal procedure. The idea is to use a fast but suboptimal bipartite graph matching algorithm as a heuristic function that estimates the future costs. The overhead for computing this heuristic function is small, and easily compensated by the speed-up achieved in tree traversal. Since the heuristic function provides us with a lower bound of the future costs, it is guaranteed to return the exact graph edit distance of two given graphs.