Finding balanced skew partitions in perfect graphs

A graph G is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one; and it is known that this is equivalent to being perfect, that is, that the chromatic number of every induced subgraph equals the size of its largest clique. A skew partition in G is a partition (A,B) of V (G) such that G[A] is not connected and G[B] is not connected; and it is balanced if an additional parity condition of paths and antipaths is satisfied. In this paper we give a polynomial-time algorithm which, with input a Berge graph, outputs a balanced skew partition if there is one.

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