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In this paper, an algorithm for determining 3-colorability, i.e. the decisionproblem (YES/NO), in planar graphs is presented. The algorithm, although notexact (it could produce false positives) has two very important features: (i)it has polynomial complexity and (ii) for every "NO" answer, a "short" proof isgenerated, which is of much interest since 3-colorability is a NP-completeproblem and thus its complementary problem is in Co-NP. Hence the algorithm isexact when it determines that a given planar graph is not 3-colorable sincethis is verifiable via an automatic generation of short formal proofs (alsohuman-readable).

A polynomial 3-colorability algorithm with automatic generation of NO 3-colorability (i.e. Co-NP) short proofs