  We address necklace solitons supported by circular waveguide arrays with
out-of-phase modulation of nonlinearity and linear refractive index. Such
two-dimensional necklace solitons appear as rings of multiple out-of-phase
bright spots. We show that necklace solitons are stable if their peak intensity
is low or moderate and that the domain of stability shrinks with increasing
nonlinearity modulation depth. However, we find that the stability domains
expand with increasing number of necklace spots.
