Motivated by an application in condensed matter physics and quantum information theory, we prove that every non-null even-hole-free claw-free graph has a simplicial clique, that is, a clique K such that for every vertex $v\in K$, the set of neighbours of v outside of K is a clique. In fact, we prove the existence of a simplicial clique in a more general class of graphs defined by forbidden induced subgraphs.

中文翻译：

---

关于单纯派的注解

受凝聚态物理和量子信息理论中的应用的启发，我们证明了每个非零偶孔无爪无爪图都有一个单纯团，即一个团K使得对于每个顶点$v\in 钾$，在K之外的v的邻居集是一个集团。事实上，我们证明了在由禁止诱导子图定义的更一般的图类中存在单纯派。