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

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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. 
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     author = {A. V. Pastor},
     title = {On critically $3$-connected graphs with exactly two vertices of degree~3. {Part~1}},
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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/

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