Geodesic
Local structure of 5 and 6-connected graphs
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 88-96
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We prove, that if graph on $n$ vertices is mimimally and contraction critically 5-connected, then it has $4n/7$ vertices of degree 5. We also prove, that if graph on $n$ vertices is mimimally and contraction critically 6-connected, then it has $n/2$ vertices of degree 6. Bibl. 7 titles. 
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S. A. Obraztsova. Local structure of 5 and 6-connected graphs. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 88-96. http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a4/

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