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Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle.
On minimal digraphs with given girth
L. Caccetta and R. Häggkvist · 1978
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Counting subgraphs: a new approach to the Caccetta-Häggkvist conjecture
J. A. Bondy · 1997
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Directed triangles in digraphs
J. Shen · 1998
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Limits of dense graph sequences
L. Lovász and B. Szegedy · 2006
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A summary of results and problems related to the Caccetta–Häggkvist conjecture
B. Sullivan · 2006
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On directed triangles in digraphs
P. Hamburger, P. Haxell, and A. Kostochka · 2007
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Flag algebras
A. A. Razborov · 2007
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Cycles in dense digraphs
M. Chudnovsky, P. Seymour, and B. Sullivan · 2008
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On the minimal density of triangles in graphs
A. A. Razborov · 2008
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On 3-hypergraphs with forbidden 4-vertex configurations
A. A. Razborov · 2010
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Hypergraphs do jump
R. Baber and J. Talbot · 2011
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Destroying cycles in digraphs
M. Dunkum, P. Hamburger, and A. Pór · 2011
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Undecidability of linear inequalities in graph homomorphism densities
H. Hatami and S. Norine · 2011
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On the maximum number of five-cycles in a triangle-free graph
A. Grzesik · 2012
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Non-three-colorable common graphs exist
Random graphons and a weak Positivstellensatz for graphs
L. Lovász and B. Szegedy · 2012
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Monochromatic triangles in three-coloured graphs
J. Cummings, D. Král’, F. Pfender, K. Sperfeld, A. Treglown, and M. Young · 2013
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A problem of Erdős on the minimum number of k k -cliques
S. Das, H. Huang, J. Ma, H. Naves, and B. Sudakov · 2013
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On the number of pentagons in triangle-free graphs
H. Hatami, J. Hladký, D. Král’, S. Norine, and A. Razborov · 2013
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A new bound for the 2 / 3 2/3 conjecture
D. Král’, C.-H. Liu, J.-S. Sereni, P. Whalen, and Z. B. Yilma · 2013
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Minimum number of k k -cliques in graphs with bounded independence number
O. Pikhurko and E. R. Vaughan · 2013
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H. Hatami, J. Hladký, D. Král’, S. Norine, and A. Razborov · 2012
Cited alongside, same era.
On the Caccetta-Häggkvist conjecture with forbidden subgraphs
A. A. Razborov · 2013
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