Lines in Euclidean Ramsey theory
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 expo...
| Egile Nagusiak: | , |
|---|---|
| Formatua: | Journal article |
| Argitaratua: |
Springer US
2018
|
| _version_ | 1826285012980334592 |
|---|---|
| author | Conlon, D Fox, J |
| author_facet | Conlon, D Fox, J |
| author_sort | Conlon, D |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:22:29Z |
| format | Journal article |
| id | oxford-uuid:90d27ba5-bf79-4adc-a8c6-d427a978182f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:22:29Z |
| publishDate | 2018 |
| publisher | Springer US |
| record_format | dspace |
| spelling | oxford-uuid:90d27ba5-bf79-4adc-a8c6-d427a978182f2022-03-26T23:14:28ZLines in Euclidean Ramsey theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:90d27ba5-bf79-4adc-a8c6-d427a978182fSymplectic Elements at OxfordSpringer US2018Conlon, DFox, JLet 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. |
| spellingShingle | Conlon, D Fox, J Lines in Euclidean Ramsey theory |
| title | Lines in Euclidean Ramsey theory |
| title_full | Lines in Euclidean Ramsey theory |
| title_fullStr | Lines in Euclidean Ramsey theory |
| title_full_unstemmed | Lines in Euclidean Ramsey theory |
| title_short | Lines in Euclidean Ramsey theory |
| title_sort | lines in euclidean ramsey theory |
| work_keys_str_mv | AT conlond linesineuclideanramseytheory AT foxj linesineuclideanramseytheory |