Min Cut is NP-Complete for Edge Weigthed Trees

Abstract We show that the Min Cut Linear Arrangement Problem (Min Cut) is NP-complete for trees with polynomial size edge weights and derive from this the NP-completeness of Min Cut for planar graphs with maximum vertex degree 3. This is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/White Pebble Demand, and Topological Bandwidth for planar graphs with maximum vertex degree 3.

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