Grundy number on -classes

In this article, we define a new class of graphs, the fat-extended P 4 -laden graphs, and we show a polynomial time algorithm to determine the Grundy number of the graphs in this class. This result implies that the Grundy number can be found in polynomial time for any graph of the following classes: P4-reducible, extended P 4 -reducible, P 4 -sparse, extended P 4 -sparse, P 4 -extendible, P 4 -lite, P 4 -tidy, P 4 -laden and extended P 4 -laden, which are all strictly contained in the fat-extended P 4 -laden class.