Counting flags in triangle-free digraphs
Combinatorics
2017-07-31 v4
Abstract
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.
Keywords
Cite
@article{arxiv.0908.2791,
title = {Counting flags in triangle-free digraphs},
author = {Jan Hladky and Daniel Kral and Sergey Norin},
journal= {arXiv preprint arXiv:0908.2791},
year = {2017}
}
Comments
19 pages, 7 figures; this is the final version to appear in Combinatorica