Geodesic
On the structure of $k$-connected graphs
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 76-106

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For $k$-connected graph we determine a notion of block and build a block tree. These constructions generalize well known and important in graph theory notion of block for the case of $k$-connected graph. With the help of these notions we describe such set $W$ of vertices of $k$-connected graph, that one can delete from graph any subset of $W$ without less of vertex connectivity. 
@article{ZNSL_2000_266_a6,
     author = {D. V. Karpov and A. V. Pastor},
     title = {On the structure of $k$-connected graphs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {76--106},
     publisher = {mathdoc},
     volume = {266},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a6/}
}
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D. V. Karpov; A. V. Pastor. On the structure of $k$-connected graphs. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 76-106. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a6/