Geodesic
On the stability of Hamiltonian cycle problem in the graph
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1987), pp. 27-31.

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Two conditions providing the Hamiltonian stability of the graph with respect of the edge adding have been studied. 
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N. K. Khachatryan. On the stability of Hamiltonian cycle problem in the graph. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1987), pp. 27-31. http://geodesic.mathdoc.fr/item/UZERU_1987_1_a4/

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[3] V. Chvatal, “Tough Graphs and Hamiltonian Circuits”, Discrete Math., 5 (1973), 215–218 | DOI | MR | Zbl

[4] F. Kharari, Teoriya grafov, Mir, M., 1973