AI 中文总结
本研究解决了Chvátal提出的公开问题，证明识别CIS图（每个极大团与所有极大稳定集相交的图）是$\textsf{coNP}$完全的，厘清了该问题的计算复杂度。
AI 中文摘要
若图$G$的每个极大团都与每个极大稳定集相交（极大性按集合包含关系定义），则称其为CIS图。CIS图在多个方面与完美图相似，在博弈论中有重要应用。识别CIS图的复杂度是Chvátal于20世纪90年代提出的公开问题，此后学界出现了相互矛盾的猜想。我们通过证明识别CIS图是$\textsf{coNP}$完全的，解决了该问题。
英文摘要
A graph $G$ is called $CIS$ if each maximal clique intersects each maximal stable set of $G$, with maximality taken with respect to set inclusion. CIS graphs resemble perfect graphs in several respects and have interesting applications in game theory. The complexity of recognizing CIS graphs was posed as an open problem by Chvátal in the 1990s and has since led to conflicting conjectures. We settle the problem by showing that recognizing CIS graphs is $\mathsf{coNP}\text{-complete}$.
