  Phylogenetic networks are mathematical structures for modeling and
visualization of reticulation processes in the study of evolution. Galled
networks, reticulation visible networks, nearly-stable networks and
stable-child networks are the four classes of phylogenetic networks that are
recently introduced to study the topological and algorithmic aspects of
phylogenetic networks. We prove the following results.
  (1) A binary galled network with n leaves has at most 2(n-1) reticulation
nodes. (2) A binary nearly-stable network with n leaves has at most 3(n-1)
reticulation nodes. (3) A binary stable-child network with n leaves has at most
7(n-1) reticulation nodes.
