A Density Version of the Corradi-Hajnal Theorem

Dieter Rautenbach; Bruce Reed

A Density Version of the Corradi-Hajnal Theorem

Combinatorics 2014-10-03 v2

Authors: Dieter Rautenbach , Bruce Reed

Abstract

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.

Keywords

Corrádi-Hajnal theorem vertex disjoint cycles graph density extremal graph theory independent cycles

Cite

@article{arxiv.1410.0197,
  title  = {A Density Version of the Corradi-Hajnal Theorem},
  author = {Dieter Rautenbach and Bruce Reed},
  journal= {arXiv preprint arXiv:1410.0197},
  year   = {2014}
}

Comments

This paper has been withdrawn by the authors. We were told by Andrew Treglown that Justesen proved the same in 1988

Related papers

View all related →