1 research outputs found
More bounds for the Grundy number of graphs
A coloring of a graph is a partition of
into independent sets or color classes. A vertex is a Grundy
vertex if it is adjacent to at least one vertex in each color class for
every . A coloring is a Grundy coloring if every vertex is a Grundy
vertex, and the Grundy number of a graph is the maximum number
of colors in a Grundy coloring. We provide two new upper bounds on Grundy
number of a graph and a stronger version of the well-known Nordhaus-Gaddum
theorem. In addition, we give a new characterization for a -free graph by supporting a conjecture of Zaker, which says that
for any -free graph .Comment: 12 pages, 1 figure, accepted for publication in Journal of
Combinatorial Optimizatio