On Retracts, Absolute Retracts, and Folds in Cographs
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چکیده
Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the size of H. When restricted to the class of threshold graphs or to the class of trivially perfect graphs, the problem becomes tractable in polynomial time. The problem is also soluble in linear time when one cograph is given as an induced subgraph of the other. Foldings generalize retractions. We show that the problem to fold a trivially perfect graph onto a largest possible clique is NP-complete. For a threshold graph this folding number equals its chromatic number and achromatic number. We characterize the absolute retracts of cographs.
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تاریخ انتشار 2013