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For this decision problem, Valiant gave a polynomial time holographic algorithm for planar graphs of maximum degree 3, and showed that the problem is NP-complete for planar graphs of maximum degree 10. A recent result on defective graph coloring by Corr\\^ea et al. [Australas. J. Combin., 43, 2009] implies that the problem is already hard for planar graphs of maximum degree 8. 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