  Monogamy is a nonclassical property that limits the distribution of quantum
correlation among subparts of a multiparty system. We show that monogamy scores
for different quantum correlation measures are bounded above by functions of
genuine multipartite entanglement for a large majority of pure multiqubit
states. The bound is universal for all three-qubit pure states. We derive
necessary conditions to characterize the states that violate the bound, which
can also be observed by numerical simulation for a small set of states,
generated Haar uniformly. The results indicate that genuine multipartite
entanglement restricts the distribution of bipartite quantum correlations in a
multiparty system.
