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Title:Vizing's conjecture: a survey and recent results
Authors:ID Brešar, Boštjan (Author)
ID Dorbec, Paul (Author)
ID Goddard, Wayne (Author)
ID Hartnell, Bert L. (Author)
ID Henning, Michael A. (Author)
ID Klavžar, Sandi (Author)
ID Rall, Douglas F. (Author)
Files:URL http://www.imfm.si/preprinti/PDF/01099.pdf
 
Language:English
Work type:Not categorized
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Vizing's conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this paper we survey the approaches to this central conjecture from domination theory and give some new results along the way. For instance, several new properties of a minimal counterexample to the conjecture are obtained and a lower bound for the domination number is proved for products of claw-free graphs with arbitrary graphs. Open problems, questions and related conjectures are discussed throughout the paper.
Keywords:matematika, teorija grafov, kartezični produkt, dominacija, Vizingova domneva, mathematics, graph theory, Caretesian product, domination, Vizing's conjecture
Year of publishing:2009
Number of pages:str. 1-29
Numbering:Vol. 47, št. 1099
PID:20.500.12556/DKUM-51799 New window
ISSN:1318-4865
UDC:519.17
COBISS.SI-ID:15246169 New window
NUK URN:URN:SI:UM:DK:J6OZ4DZV
Publication date in DKUM:10.07.2015
Views:1365
Downloads:100
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Categories:Misc.
:
BREŠAR, Boštjan, DORBEC, Paul, GODDARD, Wayne, HARTNELL, Bert L., HENNING, Michael A., KLAVŽAR, Sandi and RALL, Douglas F., 2009, Vizing’s conjecture: a survey and recent results [online]. 2009. [Accessed 2 April 2025]. Retrieved from: http://www.imfm.si/preprinti/PDF/01099.pdf
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