Deleting to Structured Trees

We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are best modeled by full binary trees. We establish that both the edge and vertex deletion variants of the problem are \(\mathsf {NP}\)-hard. This stands in contrast to the fact that deleting edges to obtain a forest or a tree is equivalent to the problem of finding a minimum cost spanning tree, which can be solved in polynomial time. We also establish that both problems are \(\mathsf {FPT}\) by the standard parameter.