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Let G be a graph with a vertex set VG. If there exists such a partition VG = A O B that all connected components of the induced subgraph G(B) and of the complementary induced subgraph G(A) are complete graphs, orders of which do not exceed tr and fl, respectively, then G are defined to belong to (tr, fl) class of polar graphs. In this paper it is proved that the decision problem of membership in (% fl), where fl is fixed and fl > 1, is NP-complete. It is also proved that the decision problem ofdoi:10.1016/0012-365x(86)90113-5 fatcat:gavg6cgcdbetvh5kfixo3ehdcu