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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 391, Pages 90–148 (Mi znsl4570)  
This article is cited in 9 scientific papers (total in 9 papers)

The structure of decomposition of a triconnected graph

D. V. Karpov, A. V. Pastor

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (524 kB) Citations (9)
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Abstract: We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a simple structure, named complexes. The detailed description of all complexes is presented. Moreover, we prove that the structure of a hypertree could be introduced on the set of all complexes. This structure gives us a complete description of the relative disposition of the complexes.
Key words and phrases: connectivity, triconneted graphs.
Received: 14.09.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 184, Issue 5, Pages 601–628
DOI: https://doi.org/10.1007/s10958-012-0885-1
Bibliographic databases:
Document Type: Article
UDC: 519.173.1
Language: Russian
Citation: D. V. Karpov, A. V. Pastor, “The structure of decomposition of a triconnected graph”, Combinatorics and graph theory. Part III, Zap. Nauchn. Sem. POMI, 391, POMI, St. Petersburg, 2011, 90–148; J. Math. Sci. (N. Y.), 184:5 (2012), 601–628
Citation in format AMSBIB
\Bibitem{KarPas11}
\by D.~V.~Karpov, A.~V.~Pastor
\paper The structure of decomposition of a~triconnected graph
\inbook Combinatorics and graph theory. Part~III
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 391
\pages 90--148
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4570}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 5
\pages 601--628
\crossref{https://doi.org/10.1007/s10958-012-0885-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884306960}
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  • https://www.mathnet.ru/eng/znsl/v391/p90
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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