At the end of this informal introduction, let us say a few words also about three topics that will not be considered here, despite they might have fitted nicely in the context. These 'distance colorings' lead to interesting questions and results, but usually may be viewed as colorings on the k th powers of graphs, and so they are less 'restricted' than the concepts discussed here. Second, in a more general setting, the ' P -chromatic number' of a graph can be defined with respect to any hereditary property P . Terminology not defined here for particular classes of graphs and basic concepts can be found e .g. L i holds for all 1 i n .
L admits a list coloring.
The parameter k is termed the color bound. As a trivial first remark, let us note that if v n has more colors in its list than the number of its neighbors, then G is list colorable if and only if so is G -v n . Some Variations Beside the concepts introduced above, at some points we shall mention results on the following variants, too. A more general setting for k -choosability is as follows. These concepts extend to edge and total colorings in the natural way.