A következő (november 18. (péntek), 10:00, Riesz terem) kombinatorika szeminárium előadása:

Alex Cameron (University of Illinois at Chicago): Extremal Problems on Directed Hypergraphs

A ($2 \rightarrow 1$)-uniform directed hypergraph is a $3$-uniform hypergraph for which the vertices of each edge are partitioned into a tail set of size $2$ and a head set of size $1$. In other words, each edge is a pointed set of exactly $3$ vertices. For a given directed hypergraph $F$ we define the extremal number, $\text{ex}(n,F)$, as the maximum number of edges that a directed hypergraph on $n$ vertices can have without containing a copy of $F$ as a (not necessarily induced) subgraph.

In this talk, we will look at the forbidden subgraph problem for every ($2 \rightarrow 1$)-graph with exactly two edges and characterize the properties of all directed hypergraphs which have extremal numbers that are cubic in $n$. We will then generalize the notion of a uniform directed hypergraph to include models where the edges have more vertices and other kinds of orderings. We will conclude with a discussion of many interesting open problems.

Minden érdeklődőt szeretettel várunk,

Péter