2011/02/09 by Boštjan Brešar, Paul Dorbec, Wayne Goddard +4 · 1 citation
Computer Science · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Complexity and Algorithms in Graphs
paper · doi:10.1002/jgt.20565
openalex publication_date 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
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. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 46–76, 2012