An Analytic Proof of Four Color Problem

Sanjib Kumar Kuila


An analytical proof of the Four Color Conjecture has been described in this article. Kempes chain argument and Heawoods technique to prove ‘Five color theorem’ has been exploited. Success has come through the searching of special triangles, around a vertex of degree 5, for three recursions.  This proof stands on the principle of mathematical induction, so requires no computer assistance.


Maximal Planar Graph; K5; K3,3; Bigraph; Kempe’s chain; Bichain; Representative triangle

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