Geodesic
Vertex cuts in a $k$-connected graph
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 33-60

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We study the structure of $k$-vertex cuts in a $k$-vertex-connected graph. A case of a biconnected graph is described in details as an illustration for our method. 
@article{ZNSL_2006_340_a2,
     author = {D. V. Karpov},
     title = {Vertex cuts in a $k$-connected graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--60},
     publisher = {mathdoc},
     volume = {340},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a2/}
}
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D. V. Karpov. Vertex cuts in a $k$-connected graph. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 33-60. http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a2/