Martin, Barnaby and Raimondi, Franco and Chen, Taolue and Martin, Jos (2017) 'The packing chromatic number of the infinite square lattice is between 13 and 15.', Discrete applied mathematics., 225 . pp. 136-142.
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.
|Full text:||(AM) Accepted Manuscript|
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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|Publisher Web site:||https://doi.org/10.1016/j.dam.2017.03.013|
|Publisher statement:||© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/|
|Date accepted:||27 March 2017|
|Date deposited:||12 September 2017|
|Date of first online publication:||17 April 2017|
|Date first made open access:||17 April 2018|
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