Question: Graph coloring is the process where given a graph G = ( V, E ), we assign colors to each vertex of the graph such

Graph coloring is the process where given a graph G = ( V, E ), we assign colors to each vertex of the graph such that no two adjacent vertices have the same color. The minimum number of colors required to color the graph is known as the chromatic number of the graph

1. Show that determining whether a given graph can be colored using 3 colors is an NP-complete problem. You can look up the proof from available resources, but explain it in your own words. I will deduct points if the proof is an exact cut-and-paste (10)

2. Find out one type of graphs on which the chromatic number can be obtained using a poly- nomial time algorithm. Give the algorithm. Only the pseudocode would suffice. (10)

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