Graph Coloring

Graph coloring is a method of assigning colors to the points (called vertices) in a network (graph) so that no two connected points share the same color. It helps to organize or distinguish related elements without conflicts. For example, in scheduling, each task (vertex) is assigned a time slot (color), ensuring that tasks sharing resources (edges) are not scheduled simultaneously. The goal is often to use the fewest colors possible, optimizing resource or time efficiency. This technique is useful in areas like map coloring, register allocation in compilers, and frequency assignment in wireless networks.