English

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.

Keywords

Cite

@article{arxiv.0706.4101,
  title  = {Making a K_4-free graph bipartite},
  author = {Benny Sudakov},
  journal= {arXiv preprint arXiv:0706.4101},
  year   = {2007}
}
R2 v1 2026-06-21T08:42:44.941Z