Ramsey-Sperner theory

Zoltán Füredi, Jerrold R. Griggs, Andrew M. Odlyzko, James B. Shearer

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let [n] denote the n-set {1, 2,..., n}, let k, l ≥ 1 be integers. Define fl(n, k) as the minimum number f such that for every family F ⊆ 2[n] with {divides}F{divides}>f, for every k-coloring of [n], there exists a chain A1{subset not double equals}···{subset not double equals}Al+1 in F in which the set of added elements, Al+1-A1, is monochromatic. We survey the known results for l = 1. Applying them we prove for any fixed l that there exists a constant φ{symbol}l(k) such that as n→ fl(n,k)∼φ{symbol}l(k)⌊ 1 2n⌋n and φ{symbol}l(k)∼ φk 4logk as k→. Several problems remain open.

Original languageEnglish
Pages (from-to)143-152
Number of pages10
JournalDiscrete Mathematics
Volume63
Issue number2-3
DOIs
Publication statusPublished - 1987

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Ramsey-Sperner theory'. Together they form a unique fingerprint.

  • Cite this

    Füredi, Z., Griggs, J. R., Odlyzko, A. M., & Shearer, J. B. (1987). Ramsey-Sperner theory. Discrete Mathematics, 63(2-3), 143-152. https://doi.org/10.1016/0012-365X(87)90004-5