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.
Research supported by the Deutsche Forschungsgemeinschaft (DFG), Emmy Noether research group PIAF (fixed-parameter algorithms), NI 369/4.
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Dom, M., Guo, J., Hüffner, F., Niedermeier, R. (2005). Extending the Tractability Border for Closest Leaf Powers. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_35
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DOI: https://doi.org/10.1007/11604686_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
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