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A proper coloring of an undirected graph G is an assignment of colors to the vertices of G such that no two adjacent vertices have
A proper coloring of an undirected graph G is an assignment of colors to the vertices of G such that no two adjacent vertices have the same color. A c-coloring of a graph is a proper coloring that uses at most c colors. A graph that admits a c-coloring is called c-colorable. Prove that a graph with maximum degree k is (k + 1)-colorable.
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