Exact coloring

Exact coloring is a concept from graph theory. In the context of graph coloring, a graph is said to be *exactly k-colored* if it can be colored with exactly \( k \) colors such that no two adjacent vertices share the same color. In more specific terms, when we talk about exact coloring in a graph: - The graph is properly colored if adjacent vertices have different colors. - An exact coloring restricts the number of colors used to exactly \( k \).