The Sendov conjecture may be stated: If all zeros of a complex polynomial p z < < X ลฝ . ลฝ . lie in z F 1, then there is always a zero of p z , that is, a critical point of p z , in < < ลฝ . z y a F 1, where a is any zero of p z . We prove several cases for which the Sendov conjecture is true as well
Two approaches to Sendov's conjecture
โ Scribed by Julius Borcea
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 184 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0003-889X
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๐ SIMILAR VOLUMES
## Abstract For a fixed integer __n__ ฯต ฯ, a graph __G__ of chromatic number greater than __n__ is called persistent if for all __n__ + 1โchromatic graphs __H__, the products __G__ ร __H__ are __n__ + 1โchromatic graphs. Wheter all graphs of chromatic number greater than __n__ are persistent is a l
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