Dr Barnaby Martin barnaby.d.martin@durham.ac.uk
Associate Professor
The packing chromatic number of the infinite square lattice is between 13 and 15
Martin, Barnaby; Raimondi, Franco; Chen, Taolue; Martin, Jos
Authors
Franco Raimondi
Taolue Chen
Dr Barnaby Martin barnaby.d.martin@durham.ac.uk
Associate Professor
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.
Citation
Martin, B., Raimondi, F., Chen, T., & Martin, J. (2017). The packing chromatic number of the infinite square lattice is between 13 and 15. Discrete Applied Mathematics, 225, 136-142. https://doi.org/10.1016/j.dam.2017.03.013
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 27, 2017 |
Online Publication Date | Apr 17, 2017 |
Publication Date | Apr 17, 2017 |
Deposit Date | Sep 8, 2017 |
Publicly Available Date | Mar 29, 2024 |
Journal | Discrete Applied Mathematics |
Print ISSN | 0166-218X |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 225 |
Pages | 136-142 |
DOI | https://doi.org/10.1016/j.dam.2017.03.013 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright 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/
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