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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 427, Pages 89–104 (Mi znsl6045)  
About vertices of degree $6$ of $C_3$-critical minimal $6$-connected graph

A. V. Pastorab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State Polytechnical University, St. Petersburg, Russia
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Abstract: In this paper we research $C_3$-critical minimal $6$-connected graphs, i.e. such $6$-connected graphs, that lost there $6$-connectivity when we delete any edge and in which any clique on at most $3$ verticies is contained in a $6$-cutset. We prove that more than $\frac59$ of all verticies of a such graph has degree $6$.
Key words and phrases: $k$-connectivity, minimal $k$-connected graph, $C_3$-critical $k$-connected graph.
Received: 20.10.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 212, Issue 6, Pages 698–707
DOI: https://doi.org/10.1007/s10958-016-2700-x
Bibliographic databases:
Document Type: Article
UDC: 519.173.1
Language: Russian
Citation: A. V. Pastor, “About vertices of degree $6$ of $C_3$-critical minimal $6$-connected graph”, Combinatorics and graph theory. Part VII, Zap. Nauchn. Sem. POMI, 427, POMI, St. Petersburg, 2014, 89–104; J. Math. Sci. (N. Y.), 212:6 (2016), 698–707
Citation in format AMSBIB
\Bibitem{Pas14}
\by A.~V.~Pastor
\paper About vertices of degree~$6$ of $C_3$-critical minimal $6$-connected graph
\inbook Combinatorics and graph theory. Part~VII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 427
\pages 89--104
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6045}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3485320}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 212
\issue 6
\pages 698--707
\crossref{https://doi.org/10.1007/s10958-016-2700-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953385283}
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