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DOI: 10.4230/LIPIcs.SoCG.2022.33
URN: urn:nbn:de:0030-drops-160413
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16041/
Davies, James ; Keller, Chaya ; Kleist, Linda ; Smorodinsky, Shakhar ; Walczak, Bartosz
A Solution to Ringel’s Circle Problem
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Abstract
We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel’s circle problem (1959). The proof relies on a (multidimensional) version of Gallai’s theorem with polynomial constraints, which we derive from the Hales-Jewett theorem and which may be of independent interest.
BibTeX - Entry
@InProceedings{davies_et_al:LIPIcs.SoCG.2022.33,
author = {Davies, James and Keller, Chaya and Kleist, Linda and Smorodinsky, Shakhar and Walczak, Bartosz},
title = {{A Solution to Ringel’s Circle Problem}},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
pages = {33:1--33:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-227-3},
ISSN = {1868-8969},
year = {2022},
volume = {224},
editor = {Goaoc, Xavier and Kerber, Michael},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16041},
URN = {urn:nbn:de:0030-drops-160413},
doi = {10.4230/LIPIcs.SoCG.2022.33},
annote = {Keywords: circle arrangement, chromatic number, Gallai’s theorem, polynomial method}
}
| Keywords: | circle arrangement, chromatic number, Gallai’s theorem, polynomial method | |
| Seminar: | 38th International Symposium on Computational Geometry (SoCG 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.06.2022 |
