On the editing distance of graphs
Abstract
An edgeoperation 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 $\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest number of edgeoperations needed to modify $G$ into a graph from $\mathcal{G}$. In this paper, we fix a graph $H$ and consider ${\rm Forb}(n,H)$, 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 ${\rm Forb}(n,H)$, 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 selfcomplementary and exact results for several small graphs $H$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606475
 Bibcode:
 2006math......6475A
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 J. Graph Theory 58(2) (2008), pp. 123138