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

Martin, Barnaby, Raimondi, Franco ORCID: https://orcid.org/0000-0002-9508-7713, 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. ISSN 0166-218X [Article] (doi:10.1016/j.dam.2017.03.013)

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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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