A remark on a theorem of Erdős
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Publication:783233
DOI10.1007/S10474-018-0830-YzbMATH Open1449.05190arXiv1711.11061OpenAlexW2799287367MaRDI QIDQ783233
Publication date: 11 August 2020
Published in: Acta Mathematica Hungarica (Search for Journal in Brave)
Abstract: A theorem of Erdos asserts that every infinite subset of Euclidean n-space R^n has a subset of the same cardinality having no repeated distances. This theorem is generalized here as follows: If (R^n,E) is an algebraic hypergraph that does not have an infinite, complete subset, then every infinite subset of it has an independent subset of the same cardinality.
Full work available at URL: https://arxiv.org/abs/1711.11061
Hypergraphs (05C65) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Infinite graphs (05C63)
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