Density of monochromatic infinite paths

Allan Lo, Nicolás Sanhueza-Matamala, Guanghui Wang

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For any subset A⊆N, we define its upper density to be lim supn→∞|A∩{1,…,n}|/n. We prove that every 2-edge-colouring of the complete graph on N contains a monochromatic infinite path, whose vertex set has upper density at least (9+17−−√)/16≈0.82019. This improves on results of Erdos and Galvin, and of DeBiasio and McKenney.
Original languageEnglish
Article numberP4.29
JournalElectronic Journal of Combinatorics
Issue number4
Publication statusPublished - 2 Nov 2018


  • Infinite paths
  • Ramsey theory
  • Density of monochromatic subgraphs


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