Extending the Tractability Border for Closest Leaf Powers

The NP-complete Closest 4-Leaf Power problem asks, given an undirected graph, whether it can be modified by at most 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 and “completing” previous work on Closest 2-Leaf Power and Closest 3-Leaf Power, we show that Closest 4-Leaf Power is fixed-parameter tractable with respect to parameter .

• Type: Conference
• Year: 2005
• Where: WG
• Authors: Michael Dom, Jiong Guo, Falk Hüffner, Rolf Niedermeier
• Keywords: 4-leaf Power, Closest 4-leaf Power, Computer Science, Graph Vertices, WG 2005