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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2009, Volume 6, Pages 465–504 (Mi semr77)  

This article is cited in 4 scientific papers (total in 4 papers)

Research papers

A new bound on the domination number of connected cubic graphs

A. V. Kostochka, C. Stocker

Department of Mathematics, University of Illinois, Urbana, USA
Full-text PDF (477 kB) Citations (4)
References:
Abstract: In 1996, Reed proved that the domination number, $\gamma(G)$, of every $n$-vertex graph $G$ with minimum degree at least $3$ is at most $3n/8$. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper, improving an upper bound by Kostochka and Stodolsky we show that for $n>8$ the domination number of every $n$-vertex cubic connected graph is at most $\lfloor 5n/14\rfloor$. This bound is sharp for even $8<n\leq18$.
Keywords: cubic graphs, domination, connected graphs.
Received January 6, 2009, published November 24, 2009
Bibliographic databases:
Document Type: Article
UDC: 519.172.2
MSC: 05C69, 05C40, 05C35
Language: English
Citation: A. V. Kostochka, C. Stocker, “A new bound on the domination number of connected cubic graphs”, Sib. Èlektron. Mat. Izv., 6 (2009), 465–504
Citation in format AMSBIB
\Bibitem{KosSto09}
\by A.~V.~Kostochka, C.~Stocker
\paper A~new bound on the domination number of connected cubic graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2009
\vol 6
\pages 465--504
\mathnet{http://mi.mathnet.ru/semr77}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2586700}
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  • https://www.mathnet.ru/eng/semr/v6/p465
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:63
     
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