Density of monochromatic infinite paths

Research output: Contribution to journalArticlepeer-review

Authors

  • Allan Lo
  • Nicolás Sanhueza-Matamala
  • Guanghui Wang

Colleges, School and Institutes

Abstract

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.

Details

Original languageEnglish
Article numberP4.29
JournalElectronic Journal of Combinatorics
Volume25
Issue number4
Publication statusPublished - 2 Nov 2018

Keywords

  • Infinite paths, Ramsey theory, Density of monochromatic subgraphs