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# A density Corrádi-Hajnal Theorem

Published:2014-11-13

• Peter Allen,
Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK
• Julia Böttcher,
Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK
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.