A Deterministic Polynomial Kernel for Odd Cycle Transversal and Vertex Multiway Cut in Planar Graphs
Abstract
We show that Odd Cycle Transversal and Vertex Multiway Cut admit deterministic polynomial kernels when restricted to planar graphs and parameterized by the solution size. This answers a question of Saurabh. On the way to these results, we provide an efficient sparsification routine in the flavor of the sparsification routine used for the Steiner Tree problem in planar graphs [Pilipczuk et al., ACM Trans. Algorithms, 14 (2018), 53]. It differs from the previous work because it preserves the existence of low-cost subgraphs that are not necessarily Steiner trees in the original plane graph, but structures that turn into (supergraphs of) Steiner trees after adding all edges between pairs of vertices that lie on a common face. We also show connections between Vertex Multiway Cut and the Vertex Planarization problem, where the existence of a polynomial kernel remains an important open problem.
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Information & Authors
Information
Published In
SIAM Journal on Discrete Mathematics
Pages: 2387 - 2429
DOI: 10.1137/20M1353782
ISSN (online): 1095-7146
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 17 July 2020
Accepted: 7 June 2021
Published online: 18 October 2021
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Fundacja na rzecz Nauki Polskiej https://doi.org/10.13039/501100001870
Nederlandse Organisatie voor Wetenschappelijk Onderzoek https://doi.org/10.13039/501100003246
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