VIZING’S CONJECTURE: A SURVEY AND RECENT RESULTS (2009)
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BibTeX
@MISC{Bresar09vizing’sconjecture:,
author = {Bostjan Bresar and Paul Dorbec and Wayne Goddard and Bert L. Hartnell and Michael A. Henning and Sandi Klavzar and Douglas F. Rall},
title = {VIZING’S CONJECTURE: A SURVEY AND RECENT RESULTS},
year = {2009}
}
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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.
