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 nonnegative integer k, decide whether the cyclability of G is at least k, is NP-hard. We study the parametrized complexity of this problem. We prove that this problem, parameterized by k, is co-W[1]-hard and that it does not admit a polynomial kernel on planar graphs, unless NP ⊆ co-NP/poly. On the positive side, we give an FPT algorithm for planar graphs that runs in time 22O(k2log k) • n2. Our algorithm is based on a series of graph-theoretical results on cyclic linkages in planar graphs.
Original language | English (US) |
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Pages (from-to) | 511-541 |
Number of pages | 31 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 31 |
Issue number | 1 |
DOIs | |
State | Published - 2017 |
Keywords
- Cyclability
- Linkages
- Parameterized complexity
- Treewidth
ASJC Scopus subject areas
- General Mathematics