Counting flags in triangle-free digraphs
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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)05C35
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