关于图的编辑距离
On the editing distance of graphs
摘要：
图$G$上的边操作被定义为删除现有边或添加不存在的边。给定图族$\mathcal{G}$，从$G$到$\mathcal{G}$的编辑距离是将$G$修改为从$\mathcal{G}$到图所需的最小边操作数。在本文中，我们固定了一个图$H$，并考虑了${\rm Forb}(n,H)$，所有的图的集合上的$n$顶点没有诱导副本的$H$。我们提供了所有$n$-顶点图$G$上从$G$到${\rm Forb}(n,H)$的编辑距离的最大值的界，使用我们称为图$H$的{\it二进制色数}的不变量。当$H$是自补图时，我们给出了该距离的渐近紧界，并对几个小图$H$给出了精确结果。
英文摘要：
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 $\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest number of edge-operations 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 self-complementary and exact results for several small graphs $H$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
