3.2.2. Edge Chromatic Number

Try these first

1. 1.

   What is the edge chromatic number of a graph?

   Hint

   Think about how edges are related to vertices.

2. 2.

   Define maximum degree (Δ(G)).

   Hint

   Consider the most connected vertex in the graph.

3. 3.

   What does the edge chromatic number of a graph refer to?

   • The number of colors needed for vertices
   • The number of colors needed for edges
   • The maximum degree of the graph

   Hint

   Focus on what is being colored; edges or vertices.

4. 4.

   True or False: The edge chromatic number can be less than the maximum degree of a vertex.

   • True
   • False

   Hint

   Think about the implications of adjacent edges.

5. 5.

   Given a pentagon graph (5 vertices forming a cycle), what is the edge chromatic number? Prove your answer.

   Hint

   Draw the graph and try applying colors to the edges.

6. 6.

   Create a scenario with a bipartite graph and evaluate its edge chromatic number.

   Hint

   Bipartite graphs have special properties related to colors.