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

Article

Martin, B., Raimondi, F., Chen, T. and Martin, J. 2017. The packing chromatic number of the infinite square lattice is between 13 and 15. Discrete Applied Mathematics. 225, pp. 136-142. https://doi.org/10.1016/j.dam.2017.03.013
TypeArticle
TitleThe packing chromatic number of the infinite square lattice is between 13 and 15
AuthorsMartin, B., Raimondi, F., Chen, T. and Martin, J.
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.

Research GroupFoundations of Computing group
PublisherElsevier
JournalDiscrete Applied Mathematics
ISSN0166-218X
Publication dates
Online17 Apr 2017
Print10 Jul 2017
Publication process dates
Deposited15 Jun 2017
Accepted26 Mar 2017
Output statusPublished
Accepted author manuscript
License
Digital Object Identifier (DOI)https://doi.org/10.1016/j.dam.2017.03.013
LanguageEnglish
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