The packing chromatic number of the infinite square lattice is between 13 and 15
Martin, B. and Raimondi, F. and Chen, Taolue 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. ISSN 0166-218X.
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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.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | Packing chromatic number, Broadcast chromatic number, Graph colouring, SAT solving |
| School: | Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems |
| Depositing User: | Dr Taolue Chen |
| Date Deposited: | 19 Sep 2017 14:44 |
| Last Modified: | 27 Jul 2019 16:01 |
| URI: | http://eprints.bbk.ac.uk/id/eprint/19652 |
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