Coloring Graph and Four-Color Theorem

Abstract

In this research, the topic of graph coloring was addressed, which includes coloring vertices, coloring edges, and coloring faces. Some relationships between the chromatic number and some graphs were also proven, and the color number of faces was obtained for some graphs, and a historical overview of one of the most important theorems in graph theory represented by the four-color theorem, was presented. The four-color theorem is applied to the map of Iraq and then transformed the map of Iraq into a graph.