Given a graph $G$ and a positive integer $k$, the CLIQUE problem asks if $G$ contains a clique (complete subgraph) on at least $k$ vertices. This problem is long known to be NP-complete --- in fact, it was one of Karp's list of 21 NP-complete problems. My question is:
For what restricted families of graphs is CLIQUE known to be NP-complete?
I could find one such graph class with Google's help: the class of $t$-interval graphs for any $t\ge 3$ (Butman et al., TALG 2010) .
Do you know of other graph classes where this problem has been shown to be NP-complete?
 Butman, Hermelin, Lewenstein, Rawitz. Optimization problems in multiple-interval graphs. ACM Transactions on Algorithms 6(2), 2010