In this article, we consider k-way vertex cut: the problem of finding a graph separator of a given size that decomposes the graph into the maximum number of components. Our main contribution is the derivation of an efficient polynomial-time approximation scheme for the problem on planar graphs. Also, we show that k-way vertex cut is polynomially solvable on graphs of bounded treewidth and fixed-parameter tractable on planar graphs with the size of the separator as the parameter.
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- planar graph, separator, connectivity, computational complexity, approximation scheme, APPROXIMATION ALGORITHMS, BOUNDED TREEWIDTH, GRAPHS, MULTICUT