Ramsey Number of a Connected Triangle Matching

András Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

2 Citations (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

Keywords

  • Ramsey
  • triangle matching

ASJC Scopus subject areas

  • Geometry and Topology

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