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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
Version:
Publisher's version

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Publisher copy:
10.1007/s00454-018-9980-5

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Wadham College
Role:
Author
ORCID:
0000-0001-5899-1829
More from this funder
Funding agency for:
Conlon, D
Publisher:
Springer US Publisher's website
Journal:
Discrete and Computational Geometry Journal website
Volume:
61
Issue:
1
Pages:
218–225
Publication date:
2018-03-23
Acceptance date:
2018-02-06
DOI:
EISSN:
1432-0444
ISSN:
0179-5376
Pubs id:
pubs:824946
URN:
uri:90d27ba5-bf79-4adc-a8c6-d427a978182f
UUID:
uuid:90d27ba5-bf79-4adc-a8c6-d427a978182f
Local pid:
pubs:824946

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