  A pseudocircle is a simple closed curve on some surface; an arrangement of
pseudocircles is a collection of pseudocircles that pairwise intersect in
exactly two points, at which they cross. Ortner proved that an arrangement of
pseudocircles is embeddable into the sphere if and only if all of its
subarrangements of size at most four are embeddable into the sphere, and asked
if an analogous result holds for embeddability into orientable surfaces of
higher genus. We answer this question positively: An arrangement of
pseudocircles is embeddable into an orientable surface of genus~$g$ if and only
if all of its subarrangements of size at most $4g+4$ are. Moreover, this bound
is tight. We actually have similar results for a much general notion of
arrangement, which we call an \emph{arrangement of graphs}.
