Geodesic
On imperfect critical graphs with incomplete critical component
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1985), pp. 33-37 
A. S. Markosyan. On imperfect critical graphs with incomplete critical component. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1985), pp. 33-37. http://geodesic.mathdoc.fr/item/UZERU_1985_1_a4/
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     title = {On imperfect critical graphs with incomplete critical component},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we present two assertions that are collectively equivalent to the strong conjecture about imperfect graphs [1]. The article is devoted to the study of one of the statements. The previously known structure of a critical graph containing an incomplete critical component is given [2]. In conclusion, two conditions are found, each of which is necessary and sufficient for a critical graph containing an incomplete component to be an odd cycle without diagonals or its complement.

[1] S. E. Markosyan, “O gipoteze Berzha”, Prikladnaya matematika, v. I, 1981, 41–46 | MR | Zbl

[2] S. E. Markosyan, “Sovershennye i kriticheskie grafy”, DAN Arm. SSR, X:4 (1975), 218–223

[3] M. W. Padberg, “Perfect Zero-One Matrices”, Math. Program. Study, 6 (1974), 186–196 | MR

[4] C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973 | MR | Zbl

[5] L. Lovasz, “A Characterization of Perfect Graphs”, J. Comb. Theory Ser. B, 13 (1972), 95–98 | DOI | MR | Zbl