On the editing distance of graphs

Details On the editing distance of graphs On the editing distance of graphs

2006-06-19

arxiv.org/abs/math/0606475v1

J. Graph Theory 58(2) (2008), pp. 123--138

Mathematics

Combinatorics

Scientific paper

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 $\cG$, the editing distance from $G$ to $\cG$ is the smallest number of edge-operations needed to modify $G$ into a graph from $\cG$. 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 {\it 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 $H$.

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