Coloring problems are a type of mathematical challenge where the goal is to assign colors to elements of a graph, such as vertices or edges, without violating certain rules. The most common example is the graph coloring problem, where no two adjacent vertices can share the same color. This problem has applications in scheduling, map coloring, and register allocation in computer science. Another well-known variant is the map coloring problem, which involves coloring regions on a map so that no two adjacent regions have the same color. The famous Four Color Theorem states that only four colors are needed to achieve this for any planar map. These problems are studied in combinatorics and theoretical computer science.