  Throughout the last decade, we have seen much progress towards characterising
and computing the minimum hybridisation number for a set P of rooted
phylogenetic trees. Roughly speaking, this minimum quantifies the number of
hybridisation events needed to explain a set of phylogenetic trees by
simultaneously embedding them into a phylogenetic network. From a mathematical
viewpoint, the notion of agreement forests is the underpinning concept for
almost all results that are related to calculating the minimum hybridisation
number for when |P|=2. However, despite various attempts, characterising this
number in terms of agreement forests for |P|>2 remains elusive. In this paper,
we characterise the minimum hybridisation number for when P is of arbitrary
size and consists of not necessarily binary trees. Building on our previous
work on cherry-picking sequences, we first establish a new characterisation to
compute the minimum hybridisation number in the space of tree-child networks.
Subsequently, we show how this characterisation extends to the space of all
rooted phylogenetic networks. Moreover, we establish a particular hardness
result that gives new insight into some of the limitations of agreement
forests.
