About recognizing (α, β) classes of polar

Zh.A Chernyak, A.A Chernyak
1986 Discrete Mathematics  
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 of
more » ... membership in (0% 0o) is NP-complete and the corresponding search problem of constructing the polar partition is NP-equivalent. Thereby all formerly unsolved variations of the problem of recognizing (tr, fl) classes are exhausted.
doi:10.1016/0012-365x(86)90113-5 fatcat:gavg6cgcdbetvh5kfixo3ehdcu