Closest 4-leaf power is fixed-parameter tractable

The NP-complete Closest 4-Leaf Power problem asks, given an undirected graph, whether it can be modified by at most r edge insertions or deletions such that it becomes a 4-leaf power. Herein, a 4-leaf power is a graph that can be constructed by considering an unrooted tree--the 4-leaf root--with leaves one-to-one labeled by the graph vertices, where we connect two graph vertices by an edge iff their corresponding leaves are at distance at most 4 in the tree. Complementing previous work on Closest 2-Leaf Power and Closest 3-Leaf Power, we give the first algorithmic result for Closest 4-Leaf Power, showing that Closest 4-Leaf Power is fixed-parameter tractable with respect to the parameter r. Key words: fixed-parameter tractability, graph algorithm, graph modification, graph power, leaf power, forbidden subgraph characterization

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Michael Dom, Jiong Guo, Falk Hüffner, Rolf Niedermeier
• Keywords: 4-leaf Power, 4-leaf Power Problem, Closest 4-leaf Power, DAM 2008