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Title:On Vizing's conjecture
Authors:ID Brešar, Boštjan (Author)
Files:.pdf Discussiones_Mathematicae_Graph_Theory_2001_Bresar_On_Vizing_s_conjecture.pdf (126,98 KB)
MD5: 286C4062475D3BCDAD7F938289E2AA70
 
URL http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1129
 
Language:English
Work type:Scientific work
Typology:1.01 - Original Scientific Article
Organization:FKBV - Faculty of Agriculture and Life Sciences
Abstract:A dominating set D gor a graph G is a subset V(G) such that any vertex in V(G)D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product GH Vizing's conjecture states that γ(GH)γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G)=γ(H)=3.
Keywords:mathematics, graph theory, graph, Cartesian product, domination number
Publication status:Published
Publication version:Version of Record
Year of publishing:2001
Number of pages:str. 5-11
Numbering:Letn. 21, št. 1
PID:20.500.12556/DKUM-65351 New window
ISSN:1234-3099
UDC:519.17
ISSN on article:1234-3099
COBISS.SI-ID:11010137 New window
NUK URN:URN:SI:UM:DK:PXU92DXH
Publication date in DKUM:31.03.2017
Views:1520
Downloads:123
Metadata:XML DC-XML DC-RDF
Categories:Misc.
:
BREŠAR, Boštjan, 2001, On Vizing’s conjecture. Discussiones mathematicae : Graph theory [online]. 2001. Vol. 21, no. 1, p. 5–11. [Accessed 8 January 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=65351
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Record is a part of a journal

Title:Discussiones mathematicae : Graph theory
Shortened title:Discuss. Math., Graph Theory
Publisher:Technical University Press
ISSN:1234-3099
COBISS.SI-ID:7487065 New window

Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:31.03.2017

Secondary language

Language:Slovenian
Title:O Vizingovi domnevi
Abstract:Dominirajoča množica D grafa G je taka podmnožica množice V(G), za katero ima vsaka točka iz množice V(G)D kako sosedo v D; dominantno število γ(G) pa je velikost najmanjše dominirajoče množice grafa G. Za kartezični produkt grafov GH Vizingova domneva trdi, da je γ(GH)γ(G)γ(H), kjer sta G in H poljubna grafa. V članku vpeljemo nov koncept, ki posploši običajno dominacijo grafov in dokažemo, da domneva drži v promeru, ko je γ(G)=γ(H)=3.
Keywords:matematika, teorija grafov, graf, kartezični produkt, dominantno število


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