Extending perfect matchings to Gray codes with prescribed ends
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384205" target="_blank" >RIV/00216208:11320/18:10384205 - isvavai.cz</a>
Result on the web
<a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p56/pdf" target="_blank" >https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p56/pdf</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Extending perfect matchings to Gray codes with prescribed ends
Original language description
A binary (cyclic) Gray code is a (cyclic) ordering of all binary strings of the same length such that any two consecutive strings differ in a single bit. This corresponds to a Hamiltonian path (cycle) in the hypercube. Fink showed that every perfect matching in the n-dimensional hypercube Q(n) can be extended to a Hamiltonian cycle, confirming a conjecture of Kreweras. In this paper, we study the "path version" of this problem. Namely, we characterize when a perfect matching in Q(n) extends to a Hamiltonian path between two prescribed vertices of opposite parity. Furthermore, we characterize when a perfect matching in Q(n) with two faulty vertices extends to a Hamiltonian cycle. In both cases we show that for all dimensions n >= 5 the only forbidden configurations are so-called half-layers, which are certain natural obstacles. These results thus extend Kreweras' conjecture with an additional edge, or with two faulty vertices. The proof for the case n = 5 is computer-assisted.
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/GA14-10799S" target="_blank" >GA14-10799S: Hybercubic, graph and hypergraph structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Combinatorics
ISSN
1077-8926
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
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UT code for WoS article
000440230300010
EID of the result in the Scopus database
2-s2.0-85049033236