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Packings in bipartite prisms and hypercubesBrešar, Boštjan ; Klavžar, Sandi ; Rall, Douglas F.▫$2$▫-pakirno število ▫$\rho_2(G)$▫ grafa ▫$G$▫ je kardinalnost največjega ▫$2$▫-pakiranja grafa ▫$G$▫, odprto pakirno število ▫$\rho^{\rm o}(G)$▫ pa kardinalnost največjega odprtega pakiranja grafa ... ▫$G$▫, kjer je odprto pakiranje (oz. ▫$2$▫ pakiranje) množica vozlišč grafa ▫$G$▫, katerih dve (zaprti) soseščini se ne sekata. Dokazano je, da če je ▫$G$▫ dvodelen, potem je ▫$\rho^{\rm o}(G\Box K_2) = 2\rho_2(G)$▫. Za hiperkocke sta določeni spodnji meji ▫$\rho_2(Q_n) \ge 2^{n - \lfloor \log n\rfloor -1}$▫ in ▫$\rho^{\rm o}(Q_n) \ge 2^{n - \lfloor \log (n-1)\rfloor -1}$▫. Te ugotovitve so uporabljene za injektivna barvanja hiperkock. Dokazano je, da je ▫$Q_9$▫ najmanjša hiperkocka, ki ni popolno injektivno obarvljiva. Dokazano je tudi, da je ▫$\gamma_t(Q_{2^k}\times H) = 2^{2^k-k}\gamma_t(H)$▫, kjer je ▫$H$▫ poljuben graf brez izoliranih vozlišč.Source: Discrete mathematics. - ISSN 0012-365X (Vol. 347, iss. 4, [article no.] 113875, Apr. 2024, 6 str.)Type of material - article, component part ; adult, seriousPublish date - 2024Language - englishCOBISS.SI-ID - 181387523
Author
Brešar, Boštjan |
Klavžar, Sandi |
Rall, Douglas F.
Topics
2-pakirno število |
odprto pakirno število |
dvodelna prizma |
hiperkocke |
injektivno barvanje |
celotno dominacijsko število |
2-packing number |
open packing number |
bipartite prism |
hypercube |
injective coloring |
total domination number
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Author | Brešar, Boštjan ; Klavžar, Sandi ; Rall, Douglas F. |
Title | Packings in bipartite prisms and hypercubes |
Publication date | 2024-01-15 |
COBISS.SI-ID | 181387523 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International |
Embargo | Immediate publication for public |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
---|---|---|---|
Teorija grafov | P1-0297-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Strukturni, optimizacijski in algoritmični problemi v geometrijskih in topoloških predstavitvah grafov | J1-2452-2020 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Metrični problemi v grafih in hipergrafih | N1-0285-2023 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Prirejanja in barvanja povezav v kubičnih grafih | J1-3002-2021 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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source: Discrete mathematics. - ISSN 0012-365X (Vol. 347, iss. 4, [article no.] 113875, Apr. 2024, 6 str.)
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Brešar, Boštjan | 17005 |
Klavžar, Sandi | 05949 |
Rall, Douglas F. | ![]() |
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