Abstract
The cyclability of a graph is the maximum integer k for which every k vertices lie on a cycle. The algorithmic version of the problem, given a graph G and a non-negative integer k, decide whether the cyclability of G is at least k, is NP-hard. We prove that this problem, parameterized by k, is co-W[1]-hard. We give an FPT algorithm for planar graphs that runs in time 2 2O(k2 log k) · n2. Our algorithm is based on a series of graph theoretical results on cyclic linkages in planar graphs. © 2014 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
Golovach, P. A., Kamiński, M., Maniatis, S., & Thilikos, D. M. (2014). The parameterized complexity of graph cyclability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8737 LNCS, pp. 492–504). Springer Verlag. https://doi.org/10.1007/978-3-662-44777-2_41
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