  Phylogenetic networks generalize phylogenetic trees by allowing the
modelization of events of reticulate evolution. Among the different kinds of
phylogenetic networks that have been proposed in the literature, the subclass
of binary tree-child networks is one of the most studied ones. However, very
little is known about the combinatorial structure of these networks. In this
paper we address the problem of generating all possible binary tree-child
networks with a given number of leaves in an efficient way via
reduction/augmentation operations that extend and generalize analogous
operations for phylogenetic trees and are biologically relevant. Since our
solution is recursive, this also provides us with a recurrence relation giving
an upper bound on the number of such networks.
