A relation algebra atom structure
α
\alpha
is said to be strongly representable if all atomic relation algebras with that atom structure are representable. This is equivalent to saying that the complex algebra
C
m
α
\mathfrak {Cm} \alpha
is a representable relation algebra. We show that the class of all strongly representable relation algebra atom structures is not closed under ultraproducts and is therefore not elementary. This answers a question of Maddux (1982). Our proof is based on the following construction. From an arbitrary undirected, loop-free graph
Γ
\Gamma
, we construct a relation algebra atom structure
α
(
Γ
)
\alpha (\Gamma )
and prove, for infinite
Γ
\Gamma
, that
α
(
Γ
)
\alpha (\Gamma )
is strongly representable if and only if the chromatic number of
Γ
\Gamma
is infinite. A construction of Erdös shows that there are graphs
Γ
r
\Gamma _r
(
r
>
ω
r>\omega
) with infinite chromatic number, with a non-principal ultraproduct
∏
D
Γ
r
\prod _D\Gamma _r
whose chromatic number is just two. It follows that
α
(
Γ
r
)
\alpha (\Gamma _r)
is strongly representable (each
r
>
ω
r>\omega
) but
∏
D
(
α
(
Γ
r
)
)
\prod _D(\alpha (\Gamma _r))
is not.