Infinite cliques in simple and stable graphs

Suppose that G is a graph of cardinality µ⁺ with chromatic number χ(G) ≥ µ⁺. One possible reason that this could happen is if G contains a clique of size µ⁺. We prove that this is indeed the case when the edge relation is stable. When G is a random graph (which is simple but not stable), this is not true. But still if in general the complete theory of G is simple, G must contain finite cliques of unbounded sizes.