Vertex Coloring is a method used in graph theory to assign colors to the vertices of a graph. The goal is to ensure that no two adjacent vertices share the same color. This technique is useful in various applications, such as scheduling problems, where conflicts must be avoided, or in map coloring, where neighboring regions should not have the same color. The minimum number of colors needed to achieve this is called the chromatic number of the graph. Finding the chromatic number can be challenging, especially for complex graphs, and is an important problem in computer science and mathematics.