Errata
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The definition of non-degenerate is too weak. The correct definition is:
A galled network N is non-degenerate, if for every tree edge e=(u,v) there
exists a directed path of tree edges from v to some leaf w.
Additionally, each tree node is either a leaf or is the source of two or more
different tree edges.
(Pointed out by Dan Gusfield).

Additionally, to make the proof of Theorem 1 water-tight,
Lemma 2 needs to be strengthened slightly by deleting
the last part of the last line to get
.. we can assume that each of the two attachment nodes (source nodes of the
reticulate edges leading to r) are either the root node, or an internal
tree node that is the source of at least two tree edges. 

Finally, for clarity, in Theorem 1, one should replace "among all such networks"
by "among all such galled networks".