Ramsey Number of a Connected Triangle Matching

A. Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We determine the 2-color Ramsey number of a connected triangle matching c(nK3) that is any connected graph containing n vertex disjoint triangles. We obtain that R(c(nK3), c(nK3) = 7n-2 somewhat larger than in the classical result of Burr, Erdős, and Spencer for a triangle matching, R(nK3, nK3) = 5n. The motivation is to determine the Ramsey number R(C2 n, C2 n) of the square of a cycle C2 n. We apply our Ramsey result for connected triangle matchings to show that the Ramsey number of an “almost” square of a cycle C2, c n (a cycle of length n in which all but at most a constant number c of short diagonals are present) is asymptotic to 7n/3.

Original languageEnglish
Pages (from-to)109-119
Number of pages11
JournalJournal of Graph Theory
Volume83
Issue number2
DOIs
Publication statusPublished - Oct 1 2016

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Ramsey number
Triangle
Cycle
Connected graph
Disjoint
Vertex of a graph

Keywords

  • Ramsey
  • triangle matching

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Ramsey Number of a Connected Triangle Matching. / Gyárfás, A.; Sárközy, Gábor N.

In: Journal of Graph Theory, Vol. 83, No. 2, 01.10.2016, p. 109-119.

Research output: Contribution to journalArticle

Gyárfás, A. ; Sárközy, Gábor N. / Ramsey Number of a Connected Triangle Matching. In: Journal of Graph Theory. 2016 ; Vol. 83, No. 2. pp. 109-119.
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