On vertex partitions and some minor-monotone graph parameters
We study vertex partitions of graphs according to some minor-monotone graph parameters. Ding et al. [J Combin Theory Ser B 79(2) (2000), 221246] proved that some minor-monotone parameters ? are such that, any graph G with ?(G)?2 admits a vertex partition into two graphs with parameter ? at most ?(G) ? 1. Here we prove that some of these parameters ? are such that, any graph G with ?(G)?3 admits a vertex partition into three graphs with parameter ? at most ?(G) ? 2.  2010 Wiley Periodicals, Inc. J Graph Theory 66: 49-56, 2010
vertex partition minor-monotone parameters