Gray codes extending quadratic matchings

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Gray codes extending quadratic matchings

Popis výsledku v původním jazyce

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 &gt;= 9 there is a balanced matching in K(Q_n) of size Theta(2^n/sqrt(n)) that cannot be extended in this way.

Název v anglickém jazyce

Gray codes extending quadratic matchings

Popis výsledku anglicky

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 &gt;= 9 there is a balanced matching in K(Q_n) of size Theta(2^n/sqrt(n)) that cannot be extended in this way.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA14-10799S" target="_blank" >GA14-10799S: Hyperkrychlové, grafové a hypergrafové struktury</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Graph Theory

ISSN

0364-9024

e-ISSN

—

Svazek periodika

90

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

123-136

Kód UT WoS článku

000463968200002

EID výsledku v databázi Scopus

2-s2.0-85049023638