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%2F20%3A10418932" target="_blank" >RIV/00216208:11320/20:10418932 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.ICALP.2020.60" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2020.60</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.60" target="_blank" >10.4230/LIPIcs.ICALP.2020.60</a>
Alternative languages
Result language
angličtina
Original language name
On the central levels problem
Original language description
The central levels problem asserts that the subgraph of the (2m+1)-dimensional hypercube induced by all bitstrings with at least m+1-???? many 1s and at most m+???? many 1s, i.e., the vertices in the middle 2???? levels, has a Hamilton cycle for any m >= 1 and 1 <= ???? <= m+1. This problem was raised independently by Savage, by Gregor and Škrekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case ???? = 1, and classical binary Gray codes, namely the case ???? = 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 ???? consecutive levels in the n-dimensional hypercube for any n >= 1 and 1 <= ???? <= n+1. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the n-dimensional hypercube, n>= 2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-138-2
ISSN
1868-8969
e-ISSN
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Number of pages
17
Pages from-to
1-17
Publisher name
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH
Place of publication
Dagstuhl, Germany
Event location
Saarbrücken, Germany
Event date
Jul 8, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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