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