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 Corrádi and Hajnal.

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