New Bounds on the Grundy Number of Products of Graphs
✍ Scribed by Victor Campos; András Gyárfás; Frédéric Havet; Claudia Linhares Sales; Frédéric Maffray
- Book ID
- 112121094
- Publisher
- John Wiley and Sons
- Year
- 2012
- Tongue
- English
- Weight
- 507 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
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## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph
It is proved in this note that the Grundy number, r(G), and the ochromatic number, xo(G), are the same for any graph G. An n-coloring of a graph G = ( V , E ) is a f u n c t i o n f f r o m V onto N = { I , 2 , . . . , n } such that, whenever vertices id and u are adjacent, then f ( u ) f f(u). An