Extending the tractability border for closest leaf powers

Authors:
Michael Dom;Jiong Guo;Falk Hüffner;Rolf niedermeier
Affiliations:
Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany
Venue:
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Year:
2005

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Abstract

The nP-complete Closest 4-Leaf Power problem asks, given an undirected graph, whether it can be modified by at most ℓ 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 ℓ.