A note on diameter-Ramsey sets

Corsten, Jan and Frankl, Nóra (2018) A note on diameter-Ramsey sets. European Journal of Combinatorics, 71. pp. 51-54. ISSN 0195-6698

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Abstract

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
Official URL:	https://www.sciencedirect.com/journal/european-jou...
Additional Information:	© 2018 Elsevier Ltd.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	13 Jul 2018 10:04
Last Modified:	11 Sep 2025 05:35
Projects:	K119670
Funders:	National Research, Development, and Innovation Office
URI:	http://eprints.lse.ac.uk/id/eprint/89238

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