Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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}
Linking options:
  • https://www.mathnet.ru/eng/znsl4573
  • 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
    		Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:138
    Full-text PDF :47
    References:35
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024