Abstract
Given a graphG=V,E, a connected sides cutU,V\UorδUis the set of edges ofElinking all vertices ofUto all vertices ofV\Usuch that the induced subgraphsGUandGV\Uare connected. Given a positive weight functionwdefined onE, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cutΩsuch thatwΩis 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.
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