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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 4, Pages 60–65 (Mi da697)  

Perfect multiple coverings of hypercube

K. V. Vorob'ev

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: A subset $C$ of graph vertices is called a perfect $k$-multiple covering with a radius $r$ if every vertex of this graph is within distance $r$ from exactly $k$ vertices of $C$. We give a criterion based on parameters of a perfect coloring. This criterion determines whether the perfect coloring is a perfect multiple covering with fixed radius $r\geq1$ of some multiplicity. Bibliogr. 13.

Keywords: hypercube, perfect coloring, perfect code, perfect multiple coverings.

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Bibliographic databases:

Document Type: Article
UDC: 519.174
Received: 29.08.2011

Citation: K. V. Vorob'ev, “Perfect multiple coverings of hypercube”, Diskretn. Anal. Issled. Oper., 19:4 (2012), 60–65

Citation in format AMSBIB
\Bibitem{Vor12}
\by K.~V.~Vorob'ev
\paper Perfect multiple coverings of hypercube
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 4
\pages 60--65
\mathnet{http://mi.mathnet.ru/da697}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013543}


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