AI 中文总结
该研究针对有限简单图，证明与指定顶点子集相交的环所需的最少顶点数不超过顶点不相交环覆盖该子集的最大顶点数，解答了相关学者的问题，通过归约方法完成论证。
AI 中文摘要
设$G$为有限简单图，$S$是$G$的顶点子集。我们证明：与$S$相交的每个环都需包含的最少顶点数，至多等于一组顶点不相交环所覆盖的$S$的最大顶点数。这解答了Bowler、Ghorbani、Gut、Jacobs和Reich在《SIAM Journal on Discrete Mathematics》2026年第40卷988-999页提出的问题。通过将问题归约到他们的双向图填充-覆盖定理，该归约保持填充值不变，且将横截集投影后不会增加其基数。
英文摘要
Let $G$ be a finite simple graph and let $S\subseteq V(G)$. We prove that the minimum number of vertices meeting every cycle that intersects $S$ is at most the maximum number of vertices of $S$ covered by a collection of vertex-disjoint cycles. This answers a question posed by Bowler, Ghorbani, Gut, Jacobs, and Reich [\emph{SIAM Journal on Discrete Mathematics} \textbf{40} (2026), 988--999]. An incidence-based reduction to their bidirected packing--covering theorem preserves the packing value and projects transversals without increasing their cardinality.
