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Title:
Efficient proper embedding of a daisy cube
Authors:
ID
Vesel, Aleksander
(
Author
)
Files:
RAZ_Vesel_Aleksander_2021.pdf
(293,91 KB)
MD5: A174426B26434A2E5A542E7F9F45B11A
https://amc-journal.eu/index.php/amc/article/download/2454/1711
Language:
English
Work type:
Scientific work
Typology:
1.01 - Original Scientific Article
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
For a set ▫$X$▫ of binary words of length ▫$h$▫ the daisy cube ▫$Q_h(X)$▫ is defined as the subgraph of the hypercube ▫$Q_h$▫ induced by the set of all vertices on shortest paths that connect vertices of ▫$X$▫ with the vertex ▫$0^h$▫. A vertex in the intersection of all of these paths is a minimal vertex of a daisy cube. A graph ▫$G$▫ isomorphic to a daisy cube admits several isometric embeddings into a hypercube. We show that an isometric embedding is proper if and only if the label ▫$0^h$▫ is assigned to a minimal vertex of ▫$G$▫. This result allows us to devise an algorithm which finds a proper embedding of a graph isomorphic to a daisy cube into a hypercube in linear time.
Keywords:
daisy cube
,
partial cube
,
isometric embedding
,
proper embedding
Publication status:
Published
Publication version:
Version of Record
Publication date:
25.10.2021
Place of publishing:
Koper
Publisher:
Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
Year of publishing:
2021
Number of pages:
str. 271-282
Numbering:
Letn. 21, št. 2
PID:
20.500.12556/DKUM-91119
UDC:
519.17
ISSN on article:
1855-3966
COBISS.SI-ID:
72352259
DOI:
10.26493/1855-3974.2454.892
Publication date in DKUM:
29.11.2024
Views:
130
Downloads:
7
Metadata:
Categories:
Misc.
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Record is a part of a journal
Title:
Ars mathematica contemporanea
Publisher:
Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
ISSN:
1855-3966
COBISS.SI-ID:
239049984
Document is financed by a project
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
P1-0297-2015
Name:
Teorija grafov
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-2452-2020
Name:
Strukturni, optimizacijski in algoritmični problemi v geometrijskih in topoloških predstavitvah grafov
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-9109-2018
Name:
Sodobne invariante grafov
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-1693-2019
Name:
Sodobni in novi metrični koncepti v teoriji grafov
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:
25.10.2021
Secondary language
Language:
Slovenian
Title:
Učinkovita pravilna vložitev marjetične kocke
Abstract:
Če je ▫$X$▫ neka množica binarnih besed dolžine ▫$h$▫, potem je marjetična kocka ▫$Q_h(X)$▫ definirana kot podgraf hiperkocke ▫$Q_h$▫, induciran z množico vseh točk na najkrajših poteh, ki povezujejo točke množice ▫$X$▫ s točko ▫$0^h$▫. Točka v preseku vseh teh poti je minimalna točka marjetične kocke. Graf ▫$G$▫, izomorfen marjetični kocki, ima več izometričnih vložitev v hiperkocko. Pokažemo, da je izometrična vložitev pravilna natanko tedaj, ko je oznaka ▫$0^h$▫ pripisana minimalni točki grafa ▫$G$▫. Na osnovi tega rezultata razvijemo algoritem, ki poišče pravilno vložitev grafa, izomorfnega marjetični kocki, v hiperkocko, in to v linearnem času.
Keywords:
marjetična kocka
,
delna kocka
,
izometrična vložitev
,
pravilna vložitev
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