A density Corr\'adi-Hajnal Theorem
  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 Corradi-Hajnal Theorem. 
Peter Allen, Julia B\"ottcher, Jan Hladk\'y, Diana Piguet
math.CO