, Volume 37, Issue 1, pp 49–76 | Cite as

Counting flags in triangle-free digraphs

  • Jan Hladký
  • Daniel Král’
  • Sergey Norin
Original Paper


Motivated by the Caccetta-Häggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0:3465n contains an oriented triangle. This improves the bound of 0:3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.

Mathematics Subject Classification (2000)



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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrahaCzech Republic
  2. 2.Mathematics Institute and Department of Computer ScienceUniversity of WarwickCoventryUK
  3. 3.Department of Mathematics & StatisticsMcGill UniversityMontrealCanada

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