Questions: Use graph coloring to find the smallest number of colors needed to color the map so that no regions sharing a common border are the same color. The smallest number of colors needed to color the map so that no regions sharing a common border are the same color is

Solution Steps

Identify the regions on the map and their borders. The regions are:

• Honduras
• Nicaragua
• Costa Rica
• Panama
• Colombia

Determine which regions share borders:

• Honduras shares a border with Nicaragua.
• Nicaragua shares borders with Honduras and Costa Rica.
• Costa Rica shares borders with Nicaragua and Panama.
• Panama shares borders with Costa Rica and Colombia.
• Colombia shares a border with Panama.

Apply graph coloring to ensure no two adjacent regions share the same color. Use the minimum number of colors:

1. Color Honduras with Color 1.
2. Color Nicaragua with Color 2 (since it shares a border with Honduras).
3. Color Costa Rica with Color 1 (since it shares a border with Nicaragua).
4. Color Panama with Color 2 (since it shares a border with Costa Rica).
5. Color Colombia with Color 1 (since it shares a border with Panama).

Final Answer