Geodesic
Grundy number of graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 5-18

Voir la notice de l'article provenant de la source Library of Science

The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i-1) vertices colored with each color j, 1 ≤ j ≤ i -1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally, we present an algorithm to generate all graphs for a given Grundy number.
Keywords: Grundy coloring, vertex coloring, cartesian product, graph product 
@article{DMGT_2007_27_1_a0,
     author = {Effantin, Brice and Kheddouci, Hamamache},
     title = {Grundy number of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {5--18},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a0/}
}
TY  - JOUR
AU  - Effantin, Brice
AU  - Kheddouci, Hamamache
TI  - Grundy number of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 5
EP  - 18
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a0/
LA  - en
ID  - DMGT_2007_27_1_a0
ER  - 
%0 Journal Article
%A Effantin, Brice
%A Kheddouci, Hamamache
%T Grundy number of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 5-18
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a0/
%G en
%F DMGT_2007_27_1_a0
Effantin, Brice; Kheddouci, Hamamache. Grundy number of graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 5-18. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a0/