Geodesic
Deleting vertices from a~biconnected graph with preserving biconnectinity
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 66-73

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Let $G$ be a biconnected graph and $W$ be a set which consists of inner vertices of parts-blocks of the graph $G$ and contains at least one vertex of each such part. It is proved that the graph $G-W$ is biconnected. 
@article{ZNSL_2014_427_a3,
     author = {D. V. Karpov},
     title = {Deleting vertices from a~biconnected graph with preserving biconnectinity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--73},
     publisher = {mathdoc},
     volume = {427},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a3/}
}
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D. V. Karpov. Deleting vertices from a~biconnected graph with preserving biconnectinity. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 66-73. http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a3/