  It is a known fact that, given two rooted binary phylogenetic trees, the
concept of maximum acyclic agreement forests is sufficient to compute
hybridization networks with minimum hybridization number. In this work, we
demonstrate by first presenting an algorithm and then showing its correctness,
that this concept is also sufficient in the case of multiple input trees. More
precisely, we show that for computing minimum hybridization networks for
multiple rooted binary phylogenetic trees on the same set of taxa it suffices
to take only maximum acyclic agreement forests into account. Moreover, this
article contains a proof showing that the minimum hybridization number for a
set of rooted binary phylogenetic trees on the same set of taxa can be also
computed by solving subproblems referring to common clusters of the input
trees.
