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. 
@article{ZNSL_2010_381_a4,
     author = {S. A. Obraztsova},
     title = {Local structure of~5 and 6-connected graphs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--96},
     publisher = {mathdoc},
     volume = {381},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a4/}
}
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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/