Question: The k - COLORING problem is to decide if the vertices of an undirected graph G can be colored with ( at most ) k

The k-COLORING problem is to decide if the vertices of an undirected
graph G can be colored with (at most) k colors so that no two adjacent
vertices have the same color. It is known that 3-COLORING is NPcomplete. Using this fact, prove that k-COLORING is NP-complete,
for all integers k >=4.

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