English

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

Discrete Mathematics 2011-02-01 v1 Computational Complexity Data Structures and Algorithms Combinatorics

Abstract

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).

Keywords

Cite

@article{arxiv.1101.6038,
  title  = {A polynomial 3-colorability algorithm with automatic generation of NO 3-colorability (i.e. Co-NP) short proofs},
  author = {Jose Antonio Martin H},
  journal= {arXiv preprint arXiv:1101.6038},
  year   = {2011}
}
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