AI 中文总结
该研究解决了环的诱导饱和图存在性问题，证明除长度为3的环外，所有环都存在对应的诱导饱和图，对q≥3构造了C_{2q+2}-诱导饱和图。
AI 中文摘要
若图G不含与H同构的诱导子图，但对G中任意一对顶点修改其邻接关系都会产生H的诱导副本，则称G为H-诱导饱和图。此前，当H为完全图、路径、奇环或长度不超过10的偶环时，H-诱导饱和图的存在性问题已得到解决。本文中，对任意整数q≥3，我们构造了一个C_{2q+2}-诱导饱和图。因此，除长度为3的环外，所有环都存在诱导饱和图。
英文摘要
A graph $G$ is \emph{$H$-induced-saturated} if $G$ has no induced subgraph isomorphic to $H$ but changing the adjacency of an arbitrary pair of vertices in $G$ creates an induced copy of $H$. The existence problem for $H$-induced-saturated graphs had previously been settled when $H$ is a complete graph, a path, an odd cycle, or an even cycle of length at most $10$. In this paper, for every integer $q\ge3$, we construct a $C_{2q+2}$-induced-saturated graph. Hence, induced-saturated graphs exist for all cycles, except for the cycle of length 3.
