On generalized Ramsey numbers

Wai Chee SHIU*, Peter Che Bor Lam, Yusheng Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let f1 and f2 be graph parameters. The Ramsey number r(f1 m; f2 ≥ n) is defined as the minimum integer N such that any graph G on N vertices, either f1(G) ≥ m or f2(Ḡ) ≥ n. A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t(G). We verify that (1 - o(1))(24n)1/3 ≤ r(t ≥ n; t ≥ n) ≤ (1 + o(1 ))(48n)1/3 as n → ∞.

Original languageEnglish
Pages (from-to)X383-388
JournalDiscrete Mathematics
Volume258
Issue number1-3
DOIs
Publication statusPublished - 6 Dec 2002

Scopus Subject Areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Mixed ramsey number
  • Ramsey number

Fingerprint

Dive into the research topics of 'On generalized Ramsey numbers'. Together they form a unique fingerprint.

Cite this