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Graph Coloring Problem

Please use words to describe the solution process:
Let G be a graph with n vertices that is not a complete graph. Prove that x (G) < n
HINT: If G does not contain k3 as a subgraph, then every face must have degree at least 4.

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A Graph Colouring Problem is solved. The solution is well presented. The solution was given a rating of "5" by the student who originally posted the question.