Graph coloring is a method used in mathematics and computer science 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 tasks must be assigned without conflicts, and in map coloring, where neighboring regions should not have the same color. The minimum number of colors needed to color a graph is called its chromatic number. Graph coloring can also be applied in network design and register allocation in programming, helping to optimize resources and reduce conflicts in complex systems.