Abstract
In the Vertex Cover Reconfiguration (VCR) problem, given graph \(G = (V, E)\), positive integers \(k\) and \(\ell \), 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 \(\ell \) vertex additions or removals such that each operation results in a vertex cover of size at most \(k\). Motivated by recent results establishing the \(\mathbf {W[1]}\)-hardness of VCR when parameterized by \(\ell \), we delineate the complexity of the problem restricted to various graph classes. In particular, we show that VCR remains \(\mathbf {W[1]}\)-hard on bipartite graphs, is \(\mathbf {NP}\)-hard but fixed-parameter tractable on graphs of bounded degree, and is solvable in time polynomial in \(|V(G)|\) on even-hole-free graphs and cactus graphs. We prove \(\mathbf {W[1]}\)-hardness and fixed-parameter tractability via two new problems of independent interest.
Amer E. Mouawad and Naomi Nishimura: Research supported by the Natural Science and Engineering Research Council of Canada.
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Mouawad, A.E., Nishimura, N., Raman, V. (2014). Vertex Cover Reconfiguration and Beyond. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_36
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DOI: https://doi.org/10.1007/978-3-319-13075-0_36
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