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Zap. Nauchn. Sem. POMI, 2011, Volume 391, Pages 45–78 (Mi znsl4568)  

This article is cited in 1 scientific paper (total in 1 paper)

Generalized flowers in $k$-connected graph

A. L. Glazmanab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
b Section de Mathématiques, Université de Genéve, Genéve, Suisse

Abstract: In this article we research $k$-cutsets in $k$-connected graphs. We introduce generalized flowers and prove some fundamental statements describing their structure. After this we consider generalized flowers in case $k=4$. When $k=4$ we give a complete description of $4$-cutsets lying in a generalized flower.

Key words and phrases: $k$-connected graph, $4$-connected graph, cutset.

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English version:
Journal of Mathematical Sciences (New York), 2012, 184:5, 579–594

Document Type: Article
UDC: 519.173.1
Received: 07.11.2011

Citation: A. L. Glazman, “Generalized flowers in $k$-connected graph”, Combinatorics and graph theory. Part III, Zap. Nauchn. Sem. POMI, 391, POMI, St. Petersburg, 2011, 45–78; J. Math. Sci. (N. Y.), 184:5 (2012), 579–594

Citation in format AMSBIB
\Bibitem{Gla11}
\by A.~L.~Glazman
\paper Generalized flowers in $k$-connected graph
\inbook Combinatorics and graph theory. Part~III
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 391
\pages 45--78
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4568}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 5
\pages 579--594
\crossref{https://doi.org/10.1007/s10958-012-0883-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884303189}


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    This publication is cited in the following articles:
    1. A. L. Glazman, “Generalized flowers in $k$-connected graph. Part 2”, J. Math. Sci. (N. Y.), 204:2 (2015), 185–231  mathnet  crossref
  • Записки научных семинаров ПОМИ
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