Gray codes extending quadratic matchings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10383786" target="_blank" >RIV/00216208:11320/19:10383786 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=RpudKTL58F" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=RpudKTL58F</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22371" target="_blank" >10.1002/jgt.22371</a>

Result language
angličtina
Original language name
Gray codes extending quadratic matchings
Original language description
Is it true that every matching in the n-dimensional hypercube Q_n can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey-Savage problem is affirmative for every matching of size at most n^2/16 + n/4. The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube K(Q_n) by edges of Q_n into a Hamilton cycle of K(Q_n). On the other hand, we show that for every n >= 9 there is a balanced matching in K(Q_n) of size Theta(2^n/sqrt(n)) that cannot be extended in this way.
Czech name
—
Czech description
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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)

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)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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