{"paper":{"title":"A note on diameter-Ramsey sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Corsten, N\\'ora Frankl","submitted_at":"2017-08-24T12:29:11Z","abstract_excerpt":"A finite set $A \\subset \\mathbb{R}^d$ is called $\\textit{diameter-Ramsey}$ if for every $r \\in \\mathbb N$, there exists some $n \\in \\mathbb N$ and a finite set $B \\subset \\mathbb{R}^n$ with $\\mathrm{diam}(A)=\\mathrm{diam}(B)$ such that whenever $B$ is coloured with $r$ colours, there is a monochromatic set $A' \\subset B$ which is congruent to $A$. We prove that sets of diameter $1$ with circumradius larger than $1/\\sqrt{2}$ are not diameter-Ramsey. In particular, we obtain that triangles with an angle larger than $135^\\circ$ are not diameter-Ramsey, improving a result of Frankl, Pach, Reiher a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07373","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}