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Given a graph , a connected sides cut  or  is the set of edges of  linking all vertices of  to all vertices of  such that the induced subgraphs  and  are connected. Given a positive weight function  defined on , the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut  such that  is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.

A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs