All of the following statements are false. Provide a counterexample for each one. iii. If it can be shown that there is not a proper 3-coloring of a graph G, then χ(G) = 4. iv. If G is a graph with χ(G) ≤ 4 then G is planar

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All of the following statements are false. Provide a counterexample for each one.

iii. If it can be shown that there is not a proper 3-coloring of a graph G, then χ(G) = 4.


iv. If G is a graph with χ(G) ≤ 4 then G is planar

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