Geodesic
About vertices of degree $6$ of $C_3$-critical minimal $6$-connected graph
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 89-104 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper we research $C_3$-critical minimal $6$-connected graphs, i.e. such $6$-connected graphs, that lost there $6$-connectivity when we delete any edge and in which any clique on at most $3$ verticies is contained in a $6$-cutset. We prove that more than $\frac59$ of all verticies of a such graph has degree $6$. 
@article{ZNSL_2014_427_a5,
     author = {A. V. Pastor},
     title = {About vertices of degree~$6$ of $C_3$-critical minimal $6$-connected graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--104},
     year = {2014},
     volume = {427},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a5/}
}
TY  - JOUR
AU  - A. V. Pastor
TI  - About vertices of degree $6$ of $C_3$-critical minimal $6$-connected graph
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 89
EP  - 104
VL  - 427
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a5/
LA  - ru
ID  - ZNSL_2014_427_a5
ER  - 
%0 Journal Article
%A A. V. Pastor
%T About vertices of degree $6$ of $C_3$-critical minimal $6$-connected graph
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 89-104
%V 427
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a5/
%G ru
%F ZNSL_2014_427_a5
A. V. Pastor. About vertices of degree $6$ of $C_3$-critical minimal $6$-connected graph. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 89-104. http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a5/

[1] K. Ando, S. Fujita, K. Kawarabayashi, “Minimally contraction-critically 6-connected graphs”, Discrete Mathematics, 312:3 (2012), 671–679 | DOI | MR | Zbl

[2] K. Ando, T. Iwase, “The number of vertices of degree 5 in a contraction-critically 5-connected graph”, Discrete Mathematics, 311 (2011), 1925–1939 | DOI | MR | Zbl

[3] K. Ando, A. Kaneko, K. Kawarabayashi, “Vertices of degree 6 in a contraction critically 6-connected graphs”, Discrete Mathematics, 273 (2003), 55–69 | DOI | MR | Zbl

[4] K. Ando, C. Qin, “Some structural properties of minimally contraction-critically 5-connected graphs”, Discrete Mathematics, 311 (2011), 1084–1097 | DOI | MR | Zbl

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

[6] M. Fontet, “Graphes 4-essentiels”, C. R. Acad. Se. Paris Ser. A, 287 (1978), 289–290 | MR | Zbl

[7] R. Halin, “A theorem on $n$-connected graphs”, J. Comb. Theory, 7 (1969), 150–154 | DOI | MR | Zbl

[8] M. Li, X. Yuan, J. Su, “The number of vertices of degree 7 in a contraction-critical 7-connected graph”, Discrete Mathematics, 308 (2008), 6262–6268 | DOI | MR | Zbl

[9] W. Mader, “Ecken Vom Gard $n$ in minimalen $n$-fach zusammenhangenden Graphen”, Arch. Math. (Basel), 23 (1972), 219–224 (German) | DOI | MR | Zbl

[10] W. Mader, “Zur Struktur minimal $n$-fach zusammenhängender Graphen”, Abh. Math. Sem. Univ. Hamburg, 49 (1979), 49–69 (German) | DOI | MR | Zbl

[11] W. Mader, “Generalization of critical connectivity of graphs”, Discrete Mathematics, 72 (1988), 267–283 | DOI | MR | Zbl

[12] N. Martinov, “A recursive characterization of the 4-connected graphs”, Discrete Mathematics, 84 (1990), 105–108 | DOI | MR | Zbl

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

[14] D. V. Karpov, A. V. Pastor, “O strukture $k$-svyaznogo grafa”, Zap. nauchn. semin. POMI, 266, 2000, 76–106 | MR | Zbl

[15] S. A. Obraztsova, “O lokalnoi strukture 5 i 6-svyaznykh grafov”, Zap. nauchn. semin. POMI, 381, 2010, 88–96 | MR

[16] S. A. Obraztsova, A. V. Pastor, “O lokalnoi strukture 7 i 8-svyaznykh grafov”, Zap. nauchn. semin. POMI, 381, 2010, 97–111 | MR

[17] S. A. Obraztsova, “O lokalnoi strukture 9 i 10-svyaznykh grafov”, Zap. nauchn. semin. POMI, 391, 2011, 157–197 | MR

[18] S. A. Obraztsova, A. V. Pastor, “O vershinakh stepeni $k$ minimalnykh i minimalnykh otnositelno styagivaniya $k$-svyaznykh grafov: verkhnie otsenki”, Zap. nauchn. semin. POMI, 391, 2011, 198–210 | MR