A Density Version of the Corradi-Hajnal Theorem
  For every positive integer $k$, we show that every graph of order $n$ at least $3k$ with more than $$\max\{{2k-1\choose 2}+(2k-1)(n-(2k-1)),{3k-1\choose 2}+(n-(3k-1))\}$$ edges has $k$ vertex disjoint cycles, which is a best possible density version of a theorem of Corr\'{a}di and Hajnal. 
Dieter Rautenbach and Bruce Reed
math.CO