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The M-Coloring Problem involves assigning colors to different vertices one by one, starting from vertex 0. Before assigning a color, check for safety by considering adjacent vertices' colors. If no color assignment is possible, backtrack and return false. To solve, create a recursive function that takes the graph, current index, number of vertices, and color array. If the current index is equal to the number of vertices, print the color configuration in the color array. If the function returns true, return true.

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