The limit of chromatic polynomials

Abstract We consider the large size limit of the number of q -colourings for three types of planar graph and obtain expansions for this limit in powers of ( q − 1) −1 . The methods used to derive and investigate these series are related to more general methods of investigating the Tutte polynomial used in theoretical physics. The analogy with physical problems is used to suggest investigations of the convergence properties of these series.

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