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.

翻译：我们讨论弗兰西斯和钢铁关于植物基因网络和树木的开放问题,他们给出了一种多元时间算法来决定植物基因网络(N)是否以树为基础,并造成问题:考虑到固定的树T和网络N,N是否以T为基础?我们表明,NP很难通过减少三维匹配(3DM)来决定,此外,这个问题是固定的参数可拉动的。