Abstract
In the Unordered Maximum Tree Orientation problem, a set P of paths in a tree and a parameter k is given, and we want to orient the edges in the tree such that all but at most k paths in P become directed paths. This is a more difficult variant of a well-studied problem in computational biology where the directions of paths in P are already given. We show that the parameterized complexity of the unordered version is between Edge Bipartization and Vertex Bipartization, and we give a characterization of orientable path sets in trees by forbidden substructures, which are cycles of a certain kind.
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