3.2.1. Motivation for Edge Colouring

Try these first

1. 1.

   Define edge colouring in simple terms.

   Hint

   Think about how colors help differentiate edges.

2. 2.

   What is the edge chromatic number?

   Hint

   Focus on the concept of minimization in graph properties.

3. 3.

   What is edge colouring in graph theory?

   • A method of coloring vertices
   • A method of coloring edges
   • A process to find cycles

   Hint

   Focus on what part of the graph is being colored.

4. 4.

   True or False: The Gupta-Vizing theorem provides exact values for edge chromatic numbers.

   • True
   • False

   Hint

   Think about the type of limits provided.

5. 5.

   Consider a graph with eight vertices where every vertex is connected to all others. What is the edge chromatic number, and how would you show this using edge colouring?

   Hint

   Use the concept of complete graphs to visualize.

6. 6.

   Create a real-life scenario where edge colouring is essential and detail how one would implement it.

   Hint

   Consider the implications of overlapping schedules.