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Consider the general partitioning (GP) problem defined as follows: Partition the vertices of a graph into k parts W 1 W k satisfying a polynomial time verifiable property. In particular, consider properties (introduced by T. Feder, P. Hell, S. Klein, and R. Motwani, in "Proceedings of the Annual ACM Symposium on Theory of Computing (STOC '99), 1999" and) specified by a pattern of requirements as to which W i forms a sparse or dense subgraph and which pairs W i , W j form a sparse or dense or andoi:10.1006/jagm.2001.1197 fatcat:2wbefphjrnfhtentgcokrgrocm