On Determining if Tree-based Networks Contain Fixed Trees
  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. 
Maria Anaya, Olga Anipchenko-Ulaj, Aisha Ashfaq, Joyce Chiu, Mahedi   Kaiser, Max Shoji Ohsawa, Megan Owen, Ella Pavlechko, ...
q-bio.PE cs.DS