Making a K_4-free graph bipartite
Combinatorics
2007-06-29 v1
Abstract
We show that every K_4-free graph G with n vertices can be made bipartite by deleting at most n^2/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3-partite graph with parts of size n/3. This proves an old conjecture of P. Erdos.
Cite
@article{arxiv.0706.4101,
title = {Making a K_4-free graph bipartite},
author = {Benny Sudakov},
journal= {arXiv preprint arXiv:0706.4101},
year = {2007}
}