### Abstract

Let β (G) denote the minimum number of edges to be removed from a graph G to make it bipartite. For each 3-chromatic graph F we determine a parameter ξ (F) such that for each F-free graph G on n vertices with minimum degree δ (G) ≥ 2 n / (ξ (F) + 2) + o (n) we have β (G) = o (n^{2}), while there are F-free graphs H with δ (H) ≥ ⌊ 2 n / (ξ (F) + 2) ⌋ for which β (H) = Ω (n^{2}).

Original language | English |
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Pages (from-to) | 3998-4002 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 17 |

DOIs | |

Publication status | Published - Sep 6 2008 |

### Keywords

- Bipartite graphs
- Chromatic number
- Extremal graph theory
- Odd cycles

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Łuczak, T., & Simonovits, M. (2008). On the minimum degree forcing F-free graphs to be (nearly) bipartite.

*Discrete Mathematics*,*308*(17), 3998-4002. https://doi.org/10.1016/j.disc.2007.06.047