Error Compensation in Leaf Root Problems

摘要

The k-Leaf Root problem is a particular case of graph power problems. Here, we study "error correction" versions of k-Leaf Root-that is, for instance, adding or deleting at most l edges to generate a graph that has a k-leaf root. We provide several NP-completeness results in this context, and we show that the NP-complete CLOSEST 3-Leaf Root problem (the error correction version of 3-Leaf Root) is fixed-parameter tractable with respect to the number of edge modifications in the given graph. Thus, we provide the seemingly first nontrivial positive algorithmic results in the field of error compensation for leaf root problems with k > 2. To this end, as a result of independent interest, we develop a forbidden subgraph characterization of graphs with 3-leaf roots.