Geodesic
On critically $3$-connected graphs with exactly two vertices of degree~3. Part~1
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IX, Tome 464 (2017), pp. 95-111

Voir la notice de l'article provenant de la source Math-Net.Ru

A graph $G$ is critically $3$-connected, if $G$ is $3$-connected and for any vertex $v\in V(G)$ the graph $G-v$ isn't $3$-connected. R. C. Entringer and P. J. Slater proved that any critically $3$-connected graph contains at least two vertices of degree 3. In this paper we classify all such graphs with one additional condition: two vertices of degree 3 are adjacent. The case of nonadjacent vertices of degree 3 will be investigated in the second part of the paper, which will be published later. 
@article{ZNSL_2017_464_a5,
     author = {A. V. Pastor},
     title = {On critically $3$-connected graphs with exactly two vertices of degree~3. {Part~1}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--111},
     publisher = {mathdoc},
     volume = {464},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_464_a5/}
}
TY  - JOUR
AU  - A. V. Pastor
TI  - On critically $3$-connected graphs with exactly two vertices of degree~3. Part~1
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 95
EP  - 111
VL  - 464
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_464_a5/
LA  - ru
ID  - ZNSL_2017_464_a5
ER  - 
%0 Journal Article
%A A. V. Pastor
%T On critically $3$-connected graphs with exactly two vertices of degree~3. Part~1
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 95-111
%V 464
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_464_a5/
%G ru
%F ZNSL_2017_464_a5
A. V. Pastor. On critically $3$-connected graphs with exactly two vertices of degree~3. Part~1. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IX, Tome 464 (2017), pp. 95-111. http://geodesic.mathdoc.fr/item/ZNSL_2017_464_a5/