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

TL;DR

This paper uses SAT-solvers to improve bounds on the packing chromatic number of the infinite square lattice, narrowing it down to between 13 and 15 through computational methods.

Contribution

It introduces a SAT-based approach to tighten bounds on the packing chromatic number, demonstrating the method's effectiveness and versatility.

Findings

Upper bound improved from 17 to 15

Lower bound improved from 12 to 13

SAT-solving proves effective for lattice coloring problems

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.