18.2.2. Mathematical Fact about Graph Coloring

Try these first

1. 1.

   What do we call the dots in a graph?

   Hint

   Think of the states in a map.

2. 2.

   How many colors are guaranteed to be sufficient according to the Four Color Theorem?

   Hint

   Can you name the theorem?

3. 3.

   What do we call the connection between two vertices in a graph?

   • Node
   • Edge
   • Vertex

   Hint

   Consider what links the nodes together.

4. 4.

   The Four Color Theorem states that four colors are necessary for graph coloring.

   • True
   • False

   Hint

   Remember the Four Color Theorem!

5. 5.

   Invent a new method for coloring a map with variable color constraints. How can you ensure optimization?

   Hint

   Think about graph traversal methods.

6. 6.

   Create a planar graph with a unique coloring solution using only three colors. Explain your graph choice.

   Hint

   Visualize the connections and overlaps.