Complexity and Exact Algorithms for Mulitcut

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 for UnrestrictedVertex Multicut in general graphs.