  We study RKKY interactions for magnetic impurities on graphene in situations
where the electronic spectrum is in the form of Landau levels. Two such
situations are considered: non-uniformly strained graphene, and graphene in a
real magnetic field. RKKY interactions are enhanced by the lowest Landau level,
which is shown to form electron states binding with the spin impurities and add
a strong non-perturbative contribution to pairwise impurity spin interactions
when their separation $R$ no more than the magnetic length. Beyond this
interactions are found to fall off as $1/R^3$ due to perturbative effects of
the negative energy Landau levels. Based on these results, we develop simple
mean-field theories for both systems, taking into account the fact that
typically the density of states in the lowest Landau level is much smaller than
the density of spin impurities. For the strain field case, we find that the
system is formally ferrimagnetic, but with very small net moment due to the
relatively low density of impurities binding electrons. The transition
temperature is nevertheless enhanced by them. For real fields, the system forms
a canted antiferromagnet if the field is not so strong as to pin the impurity
spins along the field. The possibility that the system in this latter case
supports a Kosterlitz-Thouless transition is discussed.
