Question: Suppose G is a connected graph with n 3 vertices such that x(G) = 3. Consider a proper 3-coloring of G with colors purple,

Suppose G is a connected graph with n 3 vertices such that x(G) = 3. Consider a proper 3-coloring of G with colors purple, yellow, and orange. Prove that there exists an orange node that has both a purple neighbor and a yellow neighbor. (FYI. two nodes are "neighbors" if are linked by an edge)

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