Editing Chromatic polynomial (section)

{{Short description|Function in algebraic graph theory}}
[[File:Chromatic polynomial of all 3-vertex graphs BW.png|thumb|250px|right|All non-isomorphic graphs on 3 vertices and their chromatic polynomials, clockwise from the top. The independent 3-set: {{math|''k''{{sup|3}}}}. An edge and a single vertex: {{math|''k''{{sup|2}}(''k'' − 1)}}. The 3-path: {{math|''k''(''k'' − 1){{sup|2}}}}. The 3-clique: {{math|''k''(''k'' − 1)(''k'' − 2)}}.]]

The '''chromatic polynomial''' is a [[graph polynomial]] studied in [[algebraic graph theory]], a branch of [[mathematics]]. It counts the number of [[graph coloring]]s as a function of the number of colors and was originally defined by [[George David Birkhoff]] to study the [[four color problem]]. It was generalised to the [[Tutte polynomial]] by [[Hassler Whitney]] and [[W. T. Tutte]], linking it to the [[Potts model]] of [[statistical physics]].