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

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

2011-01-31

arxiv.org/abs/1101.6038v1

Computer Science

Discrete Mathematics

Scientific paper

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

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