## 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 alo
A result on Vizing's conjecture
✍ Scribed by Liang Sun
- Book ID
- 108113386
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 175 KB
- Volume
- 275
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
In 1963, Vizing [Vichysl. Sistemy 9 (19631, 30-431 conjectured that y ( G X H) 2 y ( G ) y ( H ) , where G X Hdenotes the Cartesian product of graphs, and y(G) is the domination number. In this paper we define the extraction number x(G) and w e prove that ## M G ) 5 x(G) 5 y(G), and y ( G x H) 2 x
## Abstract In this paper we introduce the concept of fair reception of a graph which is related to its domination number. We prove that all graphs __G__ with a fair reception of size γ(__G__) satisfy Vizing's conjecture on the domination number of Cartesian product graphs, by which we extend the w