20.500.12556/DKUM-51799 Vizing's conjecture: a survey and recent results 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. matematika teorija grafov kartezični produkt dominacija Vizingova domneva mathematics graph theory Caretesian product domination Vizing's conjecture true false false Angleški jezik Neznan jezik Delo ni kategorizirano 2015-07-10 15:10:03 2015-07-10 15:10:03 2022-05-30 03:07:26 2019-07-11 07:28:37 2009 0 0 str. 1-29 št. 1099 Vol. 47 2009 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1318-4865 519.17 44310272 15246169 URN:SI:UM:DK:J6OZ4DZV http://www.imfm.si/preprinti/PDF/01099.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=76359 Fakulteta za naravoslovje in matematiko 0 0 0