  Tree-based phylogenetic networks, which may be roughly defined as
leaf-labeled networks built by adding arcs only between the original tree
edges, have elegant properties for modeling evolutionary histories. We answer
an open question of Francis, Semple, and Steel about the complexity of
determining how far a phylogenetic network is from being tree-based, including
non-binary phylogenetic networks. We show that finding a phylogenetic tree
covering the maximum number of nodes in a phylogenetic network can be be
computed in polynomial time via an encoding into a minimum-cost maximum flow
problem.
