The result for the grundy number on p4 classes
  Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked (affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. We can resume the problem of coherence of the network ad hoc of a problem of allocation of frequency We study a new class of graphs, the fat-extended P4 graphs, and we give a polynomial time algorithm to calculate the Grundy number of the graphs in this class. This result implies that the Grundy number can be found in polynomial time for many graphs 
Ali Mansouri and Mohamed Salim bouhlel
cs.DM math.CO