research-article

The Parameterized Complexity of Graph Cyclability

Authors:

Petr A. Golovach, Marcin Kamiński,

Spyridon Maniatis,

Dimitrios M. ThilikosAuthors Info & Claims

SIAM Journal on Discrete Mathematics, Volume 31, Issue 1

Pages 511 - 541

https://doi.org/10.1137/141000014

Published: 01 January 2017 Publication History

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 ${\sf co{-}W[1]}$-hard and that it does not admit a polynomial kernel on planar graphs, unless ${NP}\subseteq{\sf co}{-}{NP}/{poly}$. On the positive side, we give an FPT algorithm for planar graphs that runs in time $2^{2^{O(k^2\log k)}}\cdot n^2$. Our algorithm is based on a series of graph-theoretical results on cyclic linkages in planar graphs.

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Cited By

Golovach PStamoulis GThilikos D(2023)Hitting Topological Minor Models in Planar Graphs is Fixed Parameter TractableACM Transactions on Algorithms10.1145/358368819:3(1-29)Online publication date: 10-Feb-2023
https://dl.acm.org/doi/10.1145/3583688
Fomin FGolovach PStamoulis GThilikos D(2023)An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOLACM Transactions on Computation Theory10.1145/357127814:3-4(1-29)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1145/3571278
Crespelle CGolovach P(2022)Cyclability in graph classesDiscrete Applied Mathematics10.1016/j.dam.2022.01.021313:C(147-178)Online publication date: 31-May-2022
https://dl.acm.org/doi/10.1016/j.dam.2022.01.021

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cover image SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics Volume 31, Issue 1

DOI:10.1137/sjdmec.31.1

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© 2017, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2017

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Cited By

Golovach PStamoulis GThilikos D(2023)Hitting Topological Minor Models in Planar Graphs is Fixed Parameter TractableACM Transactions on Algorithms10.1145/358368819:3(1-29)Online publication date: 10-Feb-2023
https://dl.acm.org/doi/10.1145/3583688
Fomin FGolovach PStamoulis GThilikos D(2023)An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOLACM Transactions on Computation Theory10.1145/357127814:3-4(1-29)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1145/3571278
Crespelle CGolovach P(2022)Cyclability in graph classesDiscrete Applied Mathematics10.1016/j.dam.2022.01.021313:C(147-178)Online publication date: 31-May-2022
https://dl.acm.org/doi/10.1016/j.dam.2022.01.021

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