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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 391, Pages 198–210 (Mi znsl4573)  
This article is cited in 2 scientific papers (total in 2 papers)

About vertices of degree $k$ of minimally and contraction critically $k$-connected graphs: upper bounds

S. A. Obraztsovaa, A. V. Pastorb

a Nanyang Technological University, Singapore
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (246 kB) Citations (2)
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Abstract: 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 $k\geq5$.
Key words and phrases: $k$-connectivity, minimally $k$-connected, contraction critically $k$-connected, upper bounds.
Received: 29.08.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 184, Issue 5, Pages 655–661
DOI: https://doi.org/10.1007/s10958-012-0888-y
Bibliographic databases:
Document Type: Article
UDC: 519.173.1
Language: Russian
Citation: S. A. Obraztsova, A. V. Pastor, “About vertices of degree $k$ of minimally and contraction critically $k$-connected graphs: upper bounds”, Combinatorics and graph theory. Part III, Zap. Nauchn. Sem. POMI, 391, POMI, St. Petersburg, 2011, 198–210; J. Math. Sci. (N. Y.), 184:5 (2012), 655–661
Citation in format AMSBIB
\Bibitem{ObrPas11}
\by S.~A.~Obraztsova, A.~V.~Pastor
\paper About vertices of degree~$k$ of minimally and contraction critically $k$-connected graphs: upper bounds
\inbook Combinatorics and graph theory. Part~III
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 391
\pages 198--210
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4573}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 5
\pages 655--661
\crossref{https://doi.org/10.1007/s10958-012-0888-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884296641}
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  • https://www.mathnet.ru/eng/znsl/v391/p198
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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