4.6. Question 5

Try these first

1. 1.

   What is the vertex chromatic number?

   Hint

   Think of a scenario where you need to color a map.

2. 2.

   Consider two graphs F and H with chromatic numbers of 3 and 4, respectively. What can you conclude about the chromatic number of their union graph G?

   Hint

   Reflect on the concepts of overlapping colors when vertices are united.

3. 3.

   What is the vertex chromatic number of a complete graph with 5 vertices?

   • 1
   • 2
   • 5
   • 3

   Hint

   Consider the total number of vertices.

4. 4.

   True or False: The chromatic number of the union of two graphs is always equal to the sum of their individual chromatic numbers.

   • True
   • False

   Hint

   Think about how colors might overlap.

5. 5.

   Given two graphs, one with a chromatic number of 2 and another with a chromatic number of 5, explore the possible chromatic numbers of their union and explain your reasoning.

   Hint

   Reflect upon overlapping edges and colors as members join.

6. 6.

   Create a complete bipartite graph and a disconnected graph, calculate their chromatic numbers, and analyze their union chromatic number.

   Hint

   Visualize both graphs and imagine their union.