Geodesic
About vertices of degree $k$ of minimally and contraction critically $k$-connected graphs: upper bounds
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part III, Tome 391 (2011), pp. 198-210 
S. A. Obraztsova; A. V. Pastor. About vertices of degree $k$ of minimally and contraction critically $k$-connected graphs: upper bounds. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part III, Tome 391 (2011), pp. 198-210. http://geodesic.mathdoc.fr/item/ZNSL_2011_391_a8/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the article [4], R. Halin asked, what the constant $c_k$ such that any minimally and contraction critically $k$-connected graph has at least $c_k|V(G)|$ vertices of degree $k$. Exact bound for $k=4$ ($c_4=1$) and no upper bound for larger $k$ is known now. We found upper bounds for $c_k$ for $k\geq5$.

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