Geodesic
Relaxation of the famous $NP$-complete polar graphs recognition problem leading to the fast polynomial-time algorithm
Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 74-82

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Considered the class of polar graphs and some of its subclasses. Graph $G=(V,E)$ is called polar if there exist a partition $VG=A\cup B$ of its vertex set such that all connected components of subgraphs $G(B)$ and $\overline{G(A)}$ are cliques. It is known that the polar graph recognition problem is $NP$-complete. In this paper the relaxation of the mentioned problem leading to the fast polynomial-time algorithm is proposed. 
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     author = {R. A. Petrovich},
     title = {Relaxation of the famous $NP$-complete polar graphs recognition problem leading to the fast polynomial-time algorithm},
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     url = {http://geodesic.mathdoc.fr/item/TIMB_2012_20_1_a7/}
}
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R. A. Petrovich. Relaxation of the famous $NP$-complete polar graphs recognition problem leading to the fast polynomial-time algorithm. Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 74-82. http://geodesic.mathdoc.fr/item/TIMB_2012_20_1_a7/