ABSTRACT
The problems in graph colorings that have received the most attention involve coloring the vertices of a graph. A proper vertex coloring of a graph is an assignment of colors to the vertices of the graph, one color to each vertex, so that adjacent vertices are colored differently. This chapter considers a number of problems that can be analyzed and sometimes solved by modeling the situation described in the problem by a graph and defining a vertex coloring of the graph in an appropriate manner. An intersection graph of a nonempty subset is that graph whose vertices are the elements of the subset and where two vertices are adjacent if the subsets have a nonempty intersection. If the sets defining the intersection graph are closed intervals of real numbers, then the intersection graph is called an interval graph. The chapter also provides a discussion on chordal and non-chordal graphs.
