Complexity and Exact Algorithms for Mulitcut

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Introduction RVMC in Trees RVMC in Interval Graphs RVMC in General Graphs ConclusionFPT-algorithm — the two stagesStage two: Extend the legal pre-colorings of stage one with theprevious colors of C plus an additional color (e.g. yellow).
Introduction RVMC in Trees RVMC in Interval Graphs RVMC in General Graphs ConclusionFPT-algorithm — run timeThe color extension can be computed by dynamicprogramming on the tree decomposition of the input graphwith treewidth ω.TheoremGiven an undirected graph G = (V , E) with a tree decompositionof width ω, Restricted Vertex Multicut can be solved inO(|S| |S|+ω+1 · (|V | + |E|)) time, where S is the terminal set.Note: This FPT-algorithm also works <strong>for</strong> UnrestrictedVertex Multicut in general graphs.
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Complexity and Exact Algorithms for Mulitcut

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