Theory on the Structure and Coloring of Maximal Planar Graphs (1)Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture

Jin Xu

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arXiv · 1603.05130

Theory on the Structure and Coloring of Maximal Planar Graphs (1)Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture

Jin Xu

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Abstract

In this paper, two recursion formulae of chromatic polynomial of a maximal planar graph G are obtained. Moreover, the application of these formulaes to the proof of Four-Color Conjecture is investigated. By using these formulae, the proof of Four-Color Conjecture boils down to the study on a special class of graphs, viz., 4-chromatic-funnel pseudo uniquely-4-colorable maximal planar graphs.

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Jin Xu. 2016-03-11. Theory on the Structure and Coloring of Maximal Planar Graphs (1)Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture. https://arxiv.org/abs/1603.05130

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