The topic of finding the MST is not the only graph-related problem. Among others, node coloring exists. Its aim is to assign colors (numbers) to all nodes to comply with the rule that there cannot be an edge between two nodes with the same color. Of course, the number of colors should be as low as possible. Such a problem has some real-world applications, such as for coloring a map, which is the topic of the example shown later.
Note
Did you know that the nodes of each planar graph can be colored with no more than four colors? If you are interested in this topic, take a look at the four-color theorem (http://mathworld.wolfram.com/Four-ColorTheorem.html). The implementation of the coloring algorithm shown in this chapter is simple and in some cases could use more colors than really necessary.
Let's take a look at the following diagram:
The first diagram (shown on the left) presents a graph that is colored using four colors: red (index equal to 0), green (1), blue (2), and violet (3)...