"In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called 'colors' to elements of a graph subject to certain constraints."
Coloring involves assigning colors to vertices in a graph such that no two adjacent vertices have the same color. The minimum number of colors needed for a given graph is called its chromatic number.
"It is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring."
"Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color."
"A face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color."
"Vertex coloring is often used to introduce graph coloring problems since other coloring problems can be transformed into a vertex coloring instance."
"For example, an edge coloring of a graph is just a vertex coloring of its line graph."
"A face coloring of a plane graph is just a vertex coloring of its dual."
"However, non-vertex coloring problems are often stated and studied as-is. This is partly pedagogical and partly because some problems are best studied in their non-vertex form."
"The convention of using colors originates from coloring the countries of a map, where each face is literally colored."
"By planar duality, it became coloring the vertices, and in this form, it generalizes to all graphs."
"In mathematical and computer representations, it is typical to use the first few positive or non-negative integers as the 'colors'."
"The nature of the coloring problem depends on the number of colors but not on what they are."
"Graph coloring enjoys many practical applications as well as theoretical challenges."
"Beside the classical types of problems, different limitations can also be set on the graph."
"Limits can also be set on the way a color is assigned."
"Limits can even be set on the color itself."
"It has even reached popularity with the general public in the form of the popular number puzzle Sudoku."
"Graph coloring is still a very active field of research."
"Many terms used in this article are defined in Glossary of graph theory."
"Graph coloring enjoys many practical applications as well as theoretical challenges."