Editing Graph coloring (section)

=== Edge coloring ===
{{Main|Edge coloring}}

An '''edge coloring''' of a graph is a  proper coloring of the ''edges'', meaning an assignment of colors to edges so that no vertex is incident to two edges of the same color. An edge coloring with {{mvar|k}} colors is called a {{mvar|k}}-edge-coloring and is equivalent to the problem of partitioning the edge set into {{mvar|k}} [[Matching (graph theory)|matchings]]. The smallest number of colors needed for an edge coloring of a graph {{mvar|G}} is the '''chromatic index''', or '''edge chromatic number''', {{math|''{{prime|χ}}''(''G'')}}. A '''Tait coloring''' is a 3-edge coloring of a [[cubic graph]]. The [[four color theorem]] is equivalent to the assertion that every planar cubic [[bridge (graph theory)|bridgeless]] graph admits a Tait coloring.