This document discusses graph coloring and its applications. It defines graph coloring as assigning different colors to adjacent vertices in a graph. The chromatic number is the fewest colors needed to color a graph. Graph coloring can be used to color maps by representing regions as vertices and borders as edges. It has applications in scheduling exams and meetings so that conflicts are avoided. The four color theorem states that planar graphs (those that can be drawn in a plane without crossing edges) require no more than 4 colors.