Vizing’s conjecture for chordal graphs
✍ Scribed by Ron Aharoni; Tibor Szabó
- Book ID
- 108114014
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 234 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
Let 7(G) be the domination number of a graph G, and let G ×H be the direct product of graphs G and H. It is shown that for any k t> 0 there exists a graph G such that 7(G × G) ~< 7(G) 2 -k. This in particular disproves a conjecture from .
## 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
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