Question: (a). Show that a planar graph G with eight vertices and 13 edges cannot be 2-colored. (Hint: Use results in Section 1.4 to show that

(a). Show that a planar graph G with eight vertices and 13 edges cannot be 2-colored.

(Hint: Use results in Section 1.4 to show that G must contain a triangle.)

(b). Let G be a graph with every vertex of degree at least 3. Prove or give a counterexample to the assertion that at least three colors are needed to color the vertices of G.

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