ABSTRACT
Graph coloring has been one of the most popular and active areas in graph theory. This chapter discusses several interrelated problems on coloring, packing, and coverings of graphs. Ramsey problems can also be viewed as coloring problems. The coloring problems in the chapter concern the chromatic number of a graph. In recent years, several generalizations and combinations of the chromatic number and chromatic index have been introduced which are quite interesting. Packing and covering problems can be viewed as weaker versions of graph colorings. For example, packing problems concern colorings which allow some vertices (or edges) not to be colored. On the other hand, covering problems can be regarded as colorings which allow some vertices (or edges) to have more than one color, although in this case every vertex (or edge) is required to have at least one color.
