The editing distance in graphs

An edge-operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs G, the editing distance from G to G is the smallest number of edge-operations needed to modify G into a graph from G. In this paper, we fix a graph H and consider Forb(n,H), the set of all graphs on n vertices that have no induced copy of H. We provide bounds for the maximum over all n-vertex graphs G of the editing distance from G to Forb(n,H), using an invariant we call the binary chromatic number of the graph H. We give asymptotically tight bounds for that distance when H is self-complementary and exact results for several small graphs H.