The Parameterized Complexity of Graph Cyclability

Petr A. Golovach, Marcin Kamiński, Spyridon Maniatis, Dimitrios M. Thilikos
2017 SIAM Journal on Discrete Mathematics  
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 2 O(k 2 log k) · n 2 . Our algorithm is based on a series of graph theoretical results on cyclic linkages in planar graphs.
doi:10.1137/141000014 fatcat:vr5valgfkbhebbtqbh4vmumyje