RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskretn. Anal. Issled. Oper.: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (270 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.95
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}