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 
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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     author = {S. A. Obraztsova},
     title = {Local structure of~5 and 6-connected graphs},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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