6.1. Question 10: Edge Colouring in Graphs

Try these first

1. 1.

   What is edge colouring?

   Hint

   Think about how edges interact in a graph.

2. 2.

   How many edges can you colour with one colour if n is even?

   Hint

   Consider the relationship between vertices and edges.

3. 3.

   What is the maximum number of edges that can be coloured with the same colour in an even vertex graph?

   • n
   • n/2 + 1
   • n - 1

   Hint

   Remember how the count of edges relates to vertices.

4. 4.

   Is it possible to colour an odd vertex graph with fewer than n colours?

   • True
   • False

   Hint

   Consider how edges would conflict.

5. 5.

   Given a complete graph with 9 vertices, calculate the minimum number of colours needed for a proper edge colouring and justify your reasoning.

   Hint

   Visualize how edges conflict with one another.

6. 6.

   Create a colour assignment for a complete graph with 6 vertices, ensuring all edges are coloured distinctly. Provide a visual representation.

   Hint

   Draw it out to see the conflicts.