We find, for all sufficiently large $n$ and each $k$, the maximum number of edges in an $n$-vertex graph which does not contain $k+1$ vertex-disjoint triangles.
This extends a result of Moon [Canad. J. Math. 20 (1968), 96-102] which is in turn an extension of Mantel's Theorem. Our result can also be viewed as a density version of the Corrádi-Hajnal Theorem.
graph theory, Turan's Theorem, Mantel's Theorem, Corrádi-Hajnal Theorem, triangle
05C35 - Extremal problems [See also 90C35]