We prove that there exist functions $f,g:\mathbb{N}\to\mathbb{N}$ such that for all nonnegative integers $k$ and $d$, for every graph $G$, either $G$ contains $k$ cycles such that vertices of different cycles have distance greater than $d$ in $G$, or there exists a subset $X$ of vertices of $G$ with $|X|\leq f(k)$ such that $G-B_G(X,g(d))$ is a forest, where $B_G(X,r)$ denotes the set of vertices of $G$ having distance at most $r$ from a vertex of $X$.

翻译：我们证明存在函数$f,g:\mathbb{N}\to\mathbb{N}$，使得对于所有非负整数$k$和$d$，以及任意图$G$，要么$G$包含$k$个环，且不同环的顶点在$G$中的距离大于$d$；要么存在顶点子集$X\subseteq V(G)$满足$|X|\leq f(k)$，使得$G-B_G(X,g(d))$构成森林，其中$B_G(X,r)$表示$G$中与$X$内任意顶点距离不超过$r$的顶点集合。