Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903576 | European Journal of Combinatorics | 2018 | 4 Pages |
Abstract
A finite set AâRd is called diameter-Ramsey if for every râN, there exists some nâN and a finite set BâRn with diam(A)=diam(B) such that whenever B is coloured with r colours, there is a monochromatic set Aâ²âB which is congruent to A. We prove that sets of diameter 1 with circumradius larger than 1â2 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 Rödl. Furthermore, we deduce that there are simplices which are almost regular but not diameter-Ramsey.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jan Corsten, Nóra Frankl,