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https://doi.org/10.1057/9780230372467ng algorithmic problem, ., is known to be NP-complete in subcubic bipartite graphs [Le & Telle, TCS ’22] but its complexity was open in planar graphs and in cubic graphs. We settle both questions at once by showing that . is NP-complete in 3-connected cubic bipartite planar graphs or .. Prior to our
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Modern Latin America Since 1800 algorithms often find themselves doing a meticulous analysis of numerous different cases in order to identify these structures and design suitable branching rules, all done by hand. This process tends to be error prone and often the resulting algorithm may be difficult to implement in practice..In
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https://doi.org/10.1007/978-1-4614-6943-8a bag of a tree-cut decomposition. They are motivated by edge-cut width, recently introduced by Brand et al. (WG 2022). We show that edge-crossing width is equivalent to the known parameter tree-partition-width. On the other hand, .-edge-crossing width is a new parameter; tree-cut width and .-edge-c
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https://doi.org/10.1007/978-94-015-0770-7e rest of . via its four cornerpoints. We prove that if all the ladders contained in . are reduced to length 4, the treewidth remains unchanged (and that this bound is tight). Our result indicates that, when computing the treewidth of a graph, long ladders can simply be reduced, and that minimal for
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., . asks whether . has an acyclic matching of . (i.e., the number of edges) at least .. In this paper, we first prove that assuming ., there does not exist any .-approximation algorithm for . that approximates it within a constant factor when parameterized by .. Our reduction is general in the sens
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https://doi.org/10.1007/b137490 . satisfies property .. For example, if the property . is that of being a matching, being acyclic, or being disconnected, then we obtain an ., an ., and a ., respectively. In this paper, we analyze the problems of the computation of these matchings from the viewpoint of Parameterized Complexity wit
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Reference work 2018Latest editionstances to the vertices of the pair are distinct. This problem has mainly been studied on undirected graphs and has gained a lot of attention in the recent years. We focus on directed graphs, and show how to solve the problem in linear-time on digraphs whose underlying undirected graph (ignoring mul
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