Connected max cut is polynomial for graphs without K_5 e as a minor
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Given a graph G=(V, E), a connected cut δ (U) is the set of edges of E linking all vertices of U to all vertices of V U such that the induced subgraphs G[U] and G[V U] are connected. Given a positive weight function w defined on E, the connected maximum cut problem (CMAX CUT) is to find a connected cut Ω such that w(Ω) is maximum among all connected cuts. CMAX CUT is NP-hard even for planar graphs. In this paper, we prove that CMAX CUT is polynomial for graphs without K_5 e as a minor. We deduce a quadratic time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.
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