Graph Coloring
We are still trying to discover how to color the map of South America with the fewest
number of colors. Now that we have created a model of the map of South America, we
can color the model instead of the actual map.
A coloring of a simple graph is the assignment of a color to each vertex of the graph
so that no two adjacent vertices are assigned the same color.
Here are two simple graphs. Each one is repeated three times on your worksheet. Color
each of the graphs according to the instructions below. Make sure that in each situation
any vertices that are connected are not the same color.
1. Color each graph with as many colors as you can.
2. Then color each one in a different way.
3. Finally try to color the graph with the least number of colors possible.
Graph Coloring: Chromatic Number
The chromatic number of a graph is the least number of colors required to do a coloring
of a graph.
The last coloring of each of the graphs from the previous page determined the chromatic
number of each of the graphs.
Can you create a graph that has a chromatic number of 4? chromatic number of 5?