  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.

Combinatorics