On the minimum degree forcing F-free graphs to be (nearly) bipartite

Tomasz Łuczak, Miklós Simonovits

Research output: Contribution to journalArticle


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 (n2), while there are F-free graphs H with δ (H) ≥ ⌊ 2 n / (ξ (F) + 2) ⌋ for which β (H) = Ω (n2).

Original languageEnglish
Pages (from-to)3998-4002
Number of pages5
JournalDiscrete Mathematics
Issue number17
Publication statusPublished - Sep 6 2008


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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