2 research outputs found

    On disconnected cuts and separators

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    Abstract. For a connected graph G = (V, E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U ) ∪ {u} is connected. In that case U is called a minimal disconnected cut. We show that the problem of testing whether a graph has a minimal disconnected cut is NP-complete. We also show that the problem of testing whether a graph has a disconnected cut separating two specified vertices s and t is NP-complete

    2K2-Partition Problem

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