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

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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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     author = {D. V. Karpov and A. V. Pastor},
     title = {The structure of decomposition of a~triconnected graph},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_391_a5/}
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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/