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The graph coloring problem involves coloring the vertices of a graph with given colors such that no neighboring vertices have the same color. This problem can be solved using backtracking. For example, if three colors - red, green, and blue are given, we start by coloring the first vertex red. Moving on to the next vertex, we check its neighboring vertices to determine a suitable color. The process continues until all vertices are colored without violating the rule of adjacent vertices having different colors.
