  Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement graphs
of simple great-circle arrangements have chromatic number at most $3$.
Motivated by this conjecture, we study the colorability of arrangement graphs
for different classes of arrangements of (pseudo-)circles.
  In this paper the conjecture is verified for $\triangle$-saturated
pseudocircle arrangements, i.e., for arrangements where one color class of the
2-coloring of faces consists of triangles only, as well as for further classes
of (pseudo-)circle arrangements. These results are complemented by a
construction which maps $\triangle$-saturated arrangements with a pentagonal
face to arrangements with 4-chromatic 4-regular arrangement graphs. This
"corona" construction has similarities with the crowning construction
introduced by Koester (1985). Based on exhaustive experiments with small
arrangements we propose three strengthenings of the original conjecture.
  We also investigate fractional colorings. It is shown that the arrangement
graph of every arrangement $\mathcal{A}$ of pairwise intersecting pseudocircles
is "close" to being $3$-colorable. More precisely, the fractional chromatic
number $\chi_f(\mathcal{A})$ of the arrangement graph is bounded from above by
$\chi_f(\mathcal{A}) \le 3+O(\frac{1}{n})$, where $n$ is the number of
pseudocircles of $\mathcal{A}$. Furthermore, we construct an infinite family of
$4$-edge-critical $4$-regular planar graphs which are fractionally
$3$-colorable. This disproves a conjecture of Gimbel, K\"{u}ndgen, Li, and
Thomassen (2019).
