6.2. Question 11: Edge Chromatic Number of Complete Graphs

Try these first

1. 1.

   Define edge chromatic number.

   Hint

   Think about avoiding conflicts between connected edges.

2. 2.

   What is a complete graph?

   Hint

   Consider a simple graph where every point connects to every other point.

3. 3.

   What is the edge chromatic number for a complete graph with 6 vertices?

   • 5
   • 6
   • 4

   Hint

   Subtract one from the number of vertices.

4. 4.

   Can you color a complete graph with 5 vertices using only 4 colors?

   • True
   • False

   Hint

   Think about the connections between each vertex.

5. 5.

   You have a complete graph with 7 vertices. Find the minimum number of colors required and detail the coloring strategy.

   Hint

   Visualize using a diagram.

6. 6.

   Construct a complete graph with 9 vertices and describe a systematic coloring algorithm you would employ.

   Hint

   Think about how to rotate connections for maximum efficiency.