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arXiv · 1510.02374

The packing chromatic number of the infinite square lattice is between 13 and 15

Barnaby Martin·Franco Raimondi·Taolue Chen·Jos Martin
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Abstract

Using a SAT-solver on top of a partial previously-known solution we improve the upper bound of the packing chromatic number of the infinite square lattice from 17 to 15. We discuss the merits of SAT-solving for this kind of problem as well as compare the performance of different encodings. Further, we improve the lower bound from 12 to 13 again using a SAT-solver, demonstrating the versatility of this technology for our approach.

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Barnaby Martin, Franco Raimondi, Taolue Chen, Jos Martin. 2017-01-25. The packing chromatic number of the infinite square lattice is between 13 and 15. https://arxiv.org/abs/1510.02374

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