Coloring problems are a type of mathematical challenge that involves assigning colors to elements of a graph, such as vertices or edges, while adhering to specific rules. The most common example is the graph coloring problem, where the goal is to color the vertices of a graph so that no two adjacent vertices share the same color. This problem has applications in scheduling, register allocation in compilers, and frequency assignment in mobile networks. Another well-known variant is the map coloring problem, which seeks to color regions on a map so that adjacent regions have different colors. A famous result in this area is the Four Color Theorem, which states that any map can be colored using no more than four colors without adjacent regions sharing the same color. These problems are studied in combinatorics and theoretical computer science.