Geodesic
Extremal numbers for directed hypergraphs with two edges
Alex Cameron1
1University of Illinois at Chicago
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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Let a $2 \rightarrow 1$ directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph $F$, let the $n$th extremal number of $F$ be the maximum number of edges that any directed hypergraph on $n$ vertices can have without containing a copy of $F$. In 2007, Langlois, Mubayi, Sloan, and Turán determined the exact extremal number for a particular directed hypergraph and found the extremal number up to asymptotic equivalence for a second directed hypergraph. Each of these forbidden graphs had exactly two edges. In this paper, we determine the exact extremal numbers for every $2 \rightarrow 1$ directed hypergraph that has exactly two edges.
DOI : 10.37236/6507
Classification : 05C20, 05C35, 05C65, 05D99, 03B05, 03B42
Mots-clés : directed hypergraph, Horn clauses, extremal numbers

Alex Cameron  1

1 University of Illinois at Chicago 
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     title = {Extremal numbers for directed hypergraphs with two edges},
     journal = {The electronic journal of combinatorics},
     year = {2018},
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Alex Cameron. Extremal numbers for directed hypergraphs with two edges. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6507

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