The maximum edit distance from hereditary graph properties
Journal of Combinatorial Theory Series B
What is the furthest graph from a hereditary property?
Random Structures & Algorithms
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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 $\cal G$, the editing distance from G to $\cal G$ is the smallest number of edge-operations needed to modify G into a graph from $\cal G$. In this article, 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. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:123–138, 2008