Geodesic
The structure of decomposition of a triconnected graph
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part III, Tome 391 (2011), pp. 90-148 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a simple structure, named complexes. The detailed description of all complexes is presented. Moreover, we prove that the structure of a hypertree could be introduced on the set of all complexes. This structure gives us a complete description of the relative disposition of the complexes. 
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D. V. Karpov; A. V. Pastor. The structure of decomposition of a triconnected graph. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part III, Tome 391 (2011), pp. 90-148. http://geodesic.mathdoc.fr/item/ZNSL_2011_391_a5/

[1] O. Ore, Teoriya grafov, Nauka, M., 1968 ; O. Ore, Theory of graphs, 1962 | MR | MR

[2] F. Kharari, Teoriya grafov, Mir, M., 1973 ; F. Harary, Graph theory, 1969 | MR | MR

[3] W. T. Tutte, Connectivity in graphs, Univ. Toronto Press, Toronto, 1966 | MR | Zbl

[4] S. Mac Lane, “A structural characterizations of planar combinatorial graphs”, Duke Math. J., 3 (1937), 460–472 | DOI | MR | Zbl

[5] J. E. Hopcroft, R. E. Tarjan, “Dividing a graph into triconnected components”, SIAM J. Comput., 2 (1973), 135–158 | DOI | MR | Zbl

[6] W. Hohberg, “The decomposition of graphs into $k$-connected components”, Discr. Math., 109 (1992), 133–145 | DOI | MR | Zbl

[7] D. V. Karpov, A. V. Pastor, “O strukture $k$-svyaznogo grafa”, Zap. nauchn. semin. POMI, 266, 2000, 76–106 | MR | Zbl

[8] D. V. Karpov, “Bloki v $k$-svyaznykh grafakh”, Zap. nauchn. semin. POMI, 293, 2002, 59–93 | MR | Zbl

[9] D. V. Karpov, “Razdelyayuschie mnozhestva v $k$-svyaznom grafe”, Zap. nauchn. semin. POMI, 340, 2006, 33–60 | MR | Zbl

[10] W. T. Tutte, “A theory of 3-connected graphs”, Indag. Math., 23 (1961), 441–455 | MR