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Algorithms 2018, 11(2), 20; https://doi.org/10.3390/a11020020

Vertex Cover Reconfiguration and Beyond

1
Department of Informatics, University of Bergen, PB 7803, N-5020 Bergen, Norway
2
School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
3
Institute of Mathematical Sciences, Chennai 600113, India
4
Institute of Informatics, University of Warsaw, 02-097 Warsaw, Poland
This paper is an extended version of our paper published in the 25th International Symposium on Algorithms and Computation (ISAAC 2014).
The work of Sebastian Siebertz is supported by the National Science Centre of Poland via POLONEZ Grant Agreement UMO-2015/19/P/ST6/03998, which has received funding from the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie Grant Agreement No. 665778).
*
Author to whom correspondence should be addressed.
Received: 11 October 2017 / Revised: 2 February 2018 / Accepted: 7 February 2018 / Published: 9 February 2018
(This article belongs to the Special Issue Reconfiguration Problems)
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Abstract

In the Vertex Cover Reconfiguration (VCR) problem, given a graph G, positive integers k and and two vertex covers S and T of G of size at most k, we determine whether S can be transformed into T by a sequence of at most vertex additions or removals such that every operation results in a vertex cover of size at most k. Motivated by results establishing the W [ 1 ] -hardness of VCR when parameterized by , we delineate the complexity of the problem restricted to various graph classes. In particular, we show that VCR remains W [ 1 ] -hard on bipartite graphs, is NP -hard, but fixed-parameter tractable on (regular) graphs of bounded degree and more generally on nowhere dense graphs and is solvable in polynomial time on trees and (with some additional restrictions) on cactus graphs. View Full-Text
Keywords: reconfiguration; vertex cover; solution space; fixed-parameter tractability; bipartite graphs reconfiguration; vertex cover; solution space; fixed-parameter tractability; bipartite graphs
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Mouawad, A.E.; Nishimura, N.; Raman, V.; Siebertz, S. Vertex Cover Reconfiguration and Beyond. Algorithms 2018, 11, 20.

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