The generalized split probe problem

Abstract A generalized split ( k , l ) partition is a vertex set partition into at most k independent sets and l cliques. We prove that the (2, 1) partitioned probe problem is in P whereas the (2, 2) partitioned probe is NP-complete. The full complexity dichotomy into polynomial time and NP-complete for the class of generalized split partitioned probe problems establishes (2, 2) as the first NP-complete self-complementary partitioned probe problem, and answers negatively the PGC conjecture by finding a polynomial time recognition problem whose partitioned probe version is NP-complete.

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