A graph I mean an undirected one. A complete subgraph of a graph $G$ is called a clique. A maximal clique is a clique which is maximal with respect to inclusion. The clique number of $G$, written as $\omega (G)$, is the maximum size of a clique in $G$. Clearly, a finite graph has finite clique number. But my question is that:
What properties imply that an infinite graph $G$ have a finite clique number?