Counting flags in triangle-free digraphs

Details Counting flags in triangle-free digraphs Counting flags in triangle-free digraphs

2009-08-19

arxiv.org/abs/0908.2791v1

Mathematics

Combinatorics

14 pages, 2 figures

Scientific paper

Motivated by the Caccetta-Haggkvist 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.

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