Self Made Question

Question

Let G be a bipartite graph with vertex sets V1 and V2, where |V1| = 12 and |V2| = 18. Suppose that G has a perfect matching, which is a set of edges that covers all vertices in G. What is the minimum number of colors needed to properly color G such that no adjacent vertices share the same color, and how does it relate to the chromatic number of G? Justify your answer.

Answer 1

The answer will be 2.

Theorem-Every bipartite graph will always be 2 colour able

As we can divide a bipartite graph into 2 components thus we can assign 2 different colours to them