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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 450, Pages 109–150 (Mi znsl6339)  
This article is cited in 4 scientific papers (total in 4 papers)

On a decomposition of a $3$-connected graph into cyclically $4$-edge-connected components

A. V. Pastorab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia
Full-text PDF (340 kB) Citations (4)
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Abstract: A graph is called cyclically $4$-edge-connected if removing any three edges from it leads us to a graph, at most one connected component of which contains a cycle. $3$-connected graph is $4$-edge-connected iff removing any three edges from it leads us to either a connected graph or to a graph with exactly two connected components, one of which is a single-vertex one. We show, how to correspond for any $3$-connected graph a components tree, such that every component would be a $3$-connected and cyclically $4$-edge-connected graph.
Key words and phrases: connectivity, $3$-connected graph, cyclically $4$-edge-connected graph.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-9721.2016.1
14.Z50.31.0030
Russian Foundation for Basic Research 14-01-00545-а
Received: 18.11.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 232, Issue 1, Pages 61–83
DOI: https://doi.org/10.1007/s10958-018-3859-0
Bibliographic databases:
Document Type: Article
UDC: 519.173.1
Language: Russian
Citation: A. V. Pastor, “On a decomposition of a $3$-connected graph into cyclically $4$-edge-connected components”, Combinatorics and graph theory. Part VIII, Zap. Nauchn. Sem. POMI, 450, POMI, St. Petersburg, 2016, 109–150; J. Math. Sci. (N. Y.), 232:1 (2018), 61–83
Citation in format AMSBIB
\Bibitem{Pas16}
\by A.~V.~Pastor
\paper On a~decomposition of a~$3$-connected graph into cyclically $4$-edge-connected components
\inbook Combinatorics and graph theory. Part~VIII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 450
\pages 109--150
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6339}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3582955}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 1
\pages 61--83
\crossref{https://doi.org/10.1007/s10958-018-3859-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047304237}
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  • https://www.mathnet.ru/eng/znsl/v450/p109
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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