RELAXED CHROMATIC-NUMBERS OF GRAPHS

Given any family of graphs P, the P chromatic number chi(P)(G) of a graph G is the smallest number of classes into which V(G) can be partitioned such that each class induces a subgraph in P. We study this for hereditary families P of two broad types: the graphs containing no subgraph of a fixed graph H, and the graphs that are disjoint unions of subgraphs of H. We generalize results on ordinary chromatic number and we compute P chromatic number for special choices of P on special classes of graphs.