Graph coloring is a classical combinatorial problem with diverse applications, particularly in scheduling, resource allocation, and register allocation in compilers. This paper explores the theory behind graph coloring, the primary algorithms used to solve it, and how these techniques can be effectively applied to various scheduling problems. We investigate different types of graph coloring problems, such as vertex coloring, edge coloring, and coloring with constraints, and examine their relevance to real-world scheduling problems, including job scheduling, timetabling, and frequency assignment.