  We study the monogamy of arbitrary quantum entanglement measures $E$ for
tripartite quantum systems. Both sufficient and necessary conditions for $E$ to
be monogamous in terms of the $\alpha$th power of $E$ are explicitly derived.
It is shown that such monogamy of a entanglement measure $E$ only depends on
the boundedness of the solution set of certain equations. Moreover, the
monogamy conditions have been also obtained with respect to certain subsets of
quantum states for a given quantum correlation. Detailed examples are given to
illustrate our results.
