Editing Graph coloring (section)

=== Total coloring ===
{{Main|Total coloring}}

'''Total coloring''' is a type of coloring on the vertices ''and'' edges of a graph. When used without any qualification, a total coloring is always assumed to be proper in the sense that no adjacent vertices, no adjacent edges, and no edge and its end-vertices are assigned the same color. The total chromatic number {{math|''χ''{{pprime}}(''G'')}} of a graph {{mvar|G}} is the fewest colors needed in any total coloring of {{mvar|G}}.