On Determining if Tree-based Networks Contain Fixed Trees
Maria Anaya, Olga Anipchenko-Ulaj, Aisha Ashfaq, Joyce Chiu, Mahedi Kaiser, Max Shoji Ohsawa, Megan Owen, Ella Pavlechko, Katherine St. John, Shivam Suleria, Keith Thompson, Corrine Yap

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is NP-hard to decide, by reduction from 3-Dimensional Matching (3DM), and further, that the problem is fixed parameter tractable.