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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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},
     year = {2014},
     volume = {427},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a3/}
}
TY  - JOUR
AU  - D. V. Karpov
TI  - Deleting vertices from a biconnected graph with preserving biconnectinity
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 66
EP  - 73
VL  - 427
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a3/
LA  - ru
ID  - ZNSL_2014_427_a3
ER  - 
%0 Journal Article
%A D. V. Karpov
%T Deleting vertices from a biconnected graph with preserving biconnectinity
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 66-73
%V 427
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a3/
%G ru
%F ZNSL_2014_427_a3
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/

[1] G. Chartrand, A. Kaugars, D. R. Lick, “Critically $n$-connected graphs”, Proc. Amer. Math. Soc., 32 (1972), 63–68 | MR | Zbl

[2] Y. O. Hamidoune, “On critically $h$-connected simple graphs”, Discr. Math., 32 (1980), 257–262 | DOI | MR | Zbl

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

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

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

[6] F. Kharari, Teoriya grafov, Moskva, 1973

[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] D. V. Karpov, “Derevo razbieniya dvusvyaznogo grafa”, Zap. nauchn. semin. POMI, 417, 2013, 86–105

[11] A. S. Chukhnov, “Udalenie vershin iz $k$-svyaznykh grafov bez poteri $k$-svyaznosti”, Zap. nauchn. semin. POMI, 340, 2006, 103–116 | MR | Zbl