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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 340, Pages 76–86 (Mi znsl151)  
Cliques in $k$-connected graphs

S. A. Obraztsova

Saint-Petersburg State Electrotechnical University
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Abstract: The existance of $n+1$-cliques in $k$-connected graphs is studied. It is proved that in a $k$-connected graph $G$ such a clique exists provided $G$ satisfies the following conditions: (1) the vertices of any $n$-clique of $G$ lie in a $k$-separating set; (2) after removing certain pairs, each consisting of a vertex and an edge, the connectivity of the graph $G$ decreases by 2.
Received: 20.09.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 145, Issue 3, Pages 4975–4980
DOI: https://doi.org/10.1007/s10958-007-0332-x
Bibliographic databases:
UDC: 519.171.1
Language: Russian
Citation: S. A. Obraztsova, “Cliques in $k$-connected graphs”, Combinatorics and graph theory. Part I, Zap. Nauchn. Sem. POMI, 340, POMI, St. Petersburg, 2006, 76–86; J. Math. Sci. (N. Y.), 145:3 (2007), 4975–4980
Citation in format AMSBIB
\Bibitem{Obr06}
\by S.~A.~Obraztsova
\paper Cliques in $k$-connected graphs
\inbook Combinatorics and graph theory. Part~I
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 340
\pages 76--86
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl151}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2355486}
\zmath{https://zbmath.org/?q=an:1117.05083}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 145
\issue 3
\pages 4975--4980
\crossref{https://doi.org/10.1007/s10958-007-0332-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547663096}
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  • https://www.mathnet.ru/eng/znsl/v340/p76
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