Journal article
Lines in Euclidean Ramsey theory
- Abstract:
- Let ℓm be a sequence of m points on a line with consecutive points of distance one. For every natural number n, we prove the existence of a red/blue-coloring of En containing no red copy of ℓ2 and no blue copy of ℓm for any m≥2cn . This is best possible up to the constant c in the exponent. It also answers a question of Erdős et al. (J Comb Theory Ser A 14:341–363, 1973). They asked if, for every natural number n, there is a set K⊂E1 and a red/blue-coloring of En containing no red copy of ℓ2 and no blue copy of K.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 374.2KB, Terms of use)
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- Publisher copy:
- 10.1007/s00454-018-9980-5
Authors
- Publisher:
- Springer US
- Journal:
- Discrete and Computational Geometry More from this journal
- Volume:
- 61
- Issue:
- 1
- Pages:
- 218–225
- Publication date:
- 2018-03-23
- Acceptance date:
- 2018-02-06
- DOI:
- EISSN:
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1432-0444
- ISSN:
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0179-5376
- Keywords:
- Pubs id:
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pubs:824946
- UUID:
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uuid:90d27ba5-bf79-4adc-a8c6-d427a978182f
- Local pid:
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pubs:824946
- Source identifiers:
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824946
- Deposit date:
-
2018-02-16
- ARK identifier:
Terms of use
- Copyright holder:
- Conlon and Fox
- Copyright date:
- 2018
- Notes:
- © Conlon and Fox 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Licence:
- CC Attribution (CC BY)
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