Abstract
We define a new form of graph decomposition, based on forbidding a fixed bipartite graph from occurring as an induced subgraph of edges which cross a partition of the vertices. We show that the generalized join decomposition proposed by Hsu (J. Combin. Theory Ser. B 43 (1987) 70) is NP-complete, while some other decompositions which can be described in this way can be found in polynomial time.
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