Fair reception and Vizing's conjecture

Brešar, Boštjan; Rall, Douglas F.

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Title:	Fair reception and Vizing's conjecture
Authors:	ID Brešar, Boštjan (Author) ID Rall, Douglas F. (Author)
Files:	http://dx.doi.org/10.1002/jgt.20366
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	Vpeljemo koncept poštenega sprejema grafa, ki je povezan z njegovim dominantnim številom. Dokažemo, da za vse grafe, ki imajo pošten sprejem velikosti njihovega dominantnega števila, velja Vizingova domneva o dominantnem številu kartezičnega produkta grafov, s čimer posplošimo dobro znan rezultat Barcalkina in Germana o razstavljivih grafih. S kombiniranjem nav sega koncepta in rezultata Aharonija, Bergerja in Ziva dobimo alternativen dokaz izreka Aharonija in Szaba, ki pravi, da tetivni grafi zadoščajo Vizingovi domnevi. Predstavimo tudi novo neskončno družino grafov, ki zadoščajo Vizingovi domnevi.
Keywords:	matematika, teorija grafov, dominacija, kartezični produkt grafov, Vizingova domneva, mathematics, graph theory, domination, Cartesian product of graphs, Vizing's conjecture
Year of publishing:	2009
Number of pages:	str. 45-54
Numbering:	Vol. 61, no. 1
PID:	20.500.12556/DKUM-51792
UDC:	519.17
ISSN on article:	0364-9024
COBISS.SI-ID:	15170393
NUK URN:	URN:SI:UM:DK:LROY2X5Y
Publication date in DKUM:	10.07.2015
Views:	1254
Downloads:	115
Metadata:
Categories:	Misc.
:	BREŠAR, Boštjan and RALL, Douglas F., 2009, Fair reception and Vizing’s conjecture. Journal of graph theory [online]. 2009. Vol. 61, no. 1, p. 45–54. [Accessed 2 April 2025]. Retrieved from: http://dx.doi.org/10.1002/jgt.20366 Copy citation

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Record is a part of a journal

Title:	Journal of graph theory
Shortened title:	J. graph theory
Publisher:	J. Wiley & Sons
ISSN:	0364-9024
COBISS.SI-ID:	25747712

Secondary language

Language:	Unknown
Title:	Pošten sprejem in Vizingova domneva
Abstract:	We introduce the concept of fair reception of a graph which is related to its domination number. We prove that all graphs $G$ with a fair reception of size $gamma(G)$ satisfy Vizing's conjecture on the domination number of Cartesian product graphs, by which we extend the well-known result of Barcalkin and German concerning decomposable graphs. Combining our concept with a result of Aharoni, Berger and Ziv, we obtain an alternative proof of the theorem of Aharoni and Szabó that chordal graphs satisfy Vizing's conjecture. A new infinite family of graphs that satisfy Vizing's conjecture is also presented.

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