Vizing's conjecture: a survey and recent results

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

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;

Data

Language:	English
Year of publishing:	2009
Typology:	0 - Not set
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.17
COBISS:	15246169
ISSN:	1318-4865
Views:	737
Downloads:	83
Average score:	0 (0 votes)
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