Triangles in C5‐free graphs and hypergraphs of girth six

Beka Ergemlidze, Abhishek Methuku

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We introduce a new approach and prove that the maximum number of triangles in a 𝐶5 -free graph on 𝑛 vertices is at most


We show a connection to 𝑟 -uniform hypergraphs without (Berge) cycles of length less than six, and estimate their maximum possible size. Using our approach, we also (slightly) improve the previous estimate on the maximum size of an induced- 𝐶4 -free and 𝐶5 -free graph.
Original languageEnglish
Pages (from-to)26-39
JournalJournal of Graph Theory
Issue number1
Early online date26 Jul 2021
Publication statusE-pub ahead of print - 26 Jul 2021


  • Berge hypergraphs
  • generalized Turán
  • triangles


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