Monochromatic infinite paths

Paul Erdos, Fred Galvin

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Suppose the edges of the complete graph on the natural numbers are colored with 2 colors. We show that (1) there is a monochromatic infinite path whose vertex set has upper density ≥ 2 3, and (2) there is a monochromatic infinite path such that, for infinitely many n, the set {1,..., n} contains at least the first .21n vertices of the path. We also consider the analogous problems for colorings with 3 or more colors.

Original languageEnglish
Pages (from-to)59-70
Number of pages12
JournalDiscrete Mathematics
Volume113
Issue number1-3
DOIs
Publication statusPublished - Apr 5 1993

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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