Prove that if a graph G on n≥3 vertices has a unique 3-coloring, then G has at least 2n−3 edges.(A graph is 3-colorable when there exists a coloring of its vertices with 3 colors such that no two vertices of the same color are connected by an edge. The graph can be 3-colored uniquely if there do not exist vertices u and v of the graph that are painted different colors in one 3-coloring, yet are colored the same in another.) combinatorics unsolvedcombinatorics