On the central levels problem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10467258" target="_blank" >RIV/00216208:11320/23:10467258 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=U5UyvVh~93" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=U5UyvVh~93</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2022.12.008" target="_blank" >10.1016/j.jctb.2022.12.008</a>
Alternative languages
Result language
angličtina
Original language name
On the central levels problem
Original language description
The central levels problemasserts that the subgraph of the (2m + 1)-dimensional hypercube induced by all bitstrings with at least m + 1 - l many 1s and at most m + l many 1s, i.e., the vertices in the middle 2 l levels, has a Hamilton cycle for any m >= 1and 1 <= l <= m + 1. This problem was raised independently by Buck and Wiedemann, Savage, Gregor and Skrekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case l= 1, and classical binary Gray codes, namely the case l = m + 1. In this paper we present a general constructive solution of the central levels problem. Our results also imply the existence of optimal cycles through any sequence of l consecutive levels in the n-dimensional hypercube for any n >= 1and 1 <= l = n + 1. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the ndimensional hypercube, n >= 2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA19-08554S" target="_blank" >GA19-08554S: Structures and algorithms in highly symmetric graphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Combinatorial Theory. Series B
ISSN
0095-8956
e-ISSN
1096-0902
Volume of the periodical
160
Issue of the periodical within the volume
May 2023
Country of publishing house
US - UNITED STATES
Number of pages
43
Pages from-to
163-205
UT code for WoS article
001031049700001
EID of the result in the Scopus database
2-s2.0-00000000000