Vizing's conjecture: a survey and recent results

Boštjan Brešar (Avtor), Paul Dorbec (Avtor), Wayne Goddard (Avtor), Bert L. Hartnell (Avtor), Michael A. Henning (Avtor), Sandi Klavžar (Avtor), Douglas F. Rall (Avtor)

Povzetek

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.

Ključne besede

matematika;teorija grafov;kartezični produkt;dominacija;Vizingova domneva;mathematics;graph theory;Caretesian product;domination;Vizing's conjecture;

Podatki

Jezik:	Angleški jezik
Leto izida:	2009
Tipologija:	0 - Ni določena
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	519.17
COBISS:	15246169
ISSN:	1318-4865
Št. ogledov:	737
Št. prenosov:	83
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Neznan jezik
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 1-29
Letnik:	ǂVol. ǂ47
Zvezek:	ǂšt. ǂ1099
Čas izdaje:	2009
ID:	1474418