A note on diameter-Ramsey sets
Corsten, J. & Frankl, N.
(2018).
A note on diameter-Ramsey sets.
European Journal of Combinatorics,
71, 51-54.
https://doi.org/10.1016/j.ejc.2018.02.036
A finite set A⊂Rd is called diameter-Ramsey if for every r∈N, there exists some n∈N and a finite set B⊂Rn with diam(A)=diam(B) such that whenever B is coloured with r colours, there is a monochromatic set A′⊂B which is congruent to A. We prove that sets of diameter 1 with circumradius larger than 1/2–√ are not diameter-Ramsey. In particular, we obtain that triangles with an angle larger than 135∘ are not diameter-Ramsey, improving a result of Frankl, Pach, Reiher and R\"odl. Furthermore, we deduce that there are simplices which are almost regular but not diameter-Ramsey.
| Item Type | Article |
|---|---|
| Copyright holders | © 2018 Elsevier Ltd. |
| Departments | LSE > Academic Departments > Mathematics |
| DOI | 10.1016/j.ejc.2018.02.036 |
| Date Deposited | 13 Jul 2018 |
| Acceptance Date | 15 Feb 2018 |
| URI | https://researchonline.lse.ac.uk/id/eprint/89238 |
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