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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 2, Pages 75–83 (Mi da683)  

Construction of Hamiltonian cycles with a given range of directions of edges in the Boolean $n$-dimensional cube

V. N. Potapov

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: The spectrum of a Hamiltonian cycle (Gray code) in a Boolean $n$-cube is the $n$-tuple $a=(a_1,…,a_n)$, where $a_i$ is the number of edges from the $i$-th parallel class in the cycle. There exist well known necessary conditions for existence of the Gray code with the spectrum $a$: the numbers $a_i$ are even and for any $k=1,…,n$ the sum of $k$ arbitrary components of $a$ is not less than $2^k$. We prove existence of a number $N$ such that if the necessary conditions on the spectrum are sufficient for existence of a Hamiltonian cycle with such spectrum in the Boolean $N$-dimensional cube, then the above conditions are sufficient for all dimensions. Bibliogr. 10.

Keywords: Hamiltonian cycle, perfect matching, Boolean cube, Gray code.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:3, 339–345

Bibliographic databases:

UDC: 519.95
Received: 06.06.2011
Revised: 22.11.2011

Citation: V. N. Potapov, “Construction of Hamiltonian cycles with a given range of directions of edges in the Boolean $n$-dimensional cube”, Diskretn. Anal. Issled. Oper., 19:2 (2012), 75–83; J. Appl. Industr. Math., 6:3 (2012), 339–345

Citation in format AMSBIB
\Bibitem{Pot12}
\by V.~N.~Potapov
\paper Construction of Hamiltonian cycles with a~given range of directions of edges in the Boolean $n$-dimensional cube
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 2
\pages 75--83
\mathnet{http://mi.mathnet.ru/da683}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978613}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 339--345
\crossref{https://doi.org/10.1134/S1990478912030088}


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