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A Steiner triple system is a 3-uniform hypergraph in which every pair of vertices is contained in exactly one edge. A linear cycle (also called loose cycle) length $t$ consists of $2t$ cyclically ...

As usual, for an $r$-uniform hypergraph $G$, denote by $ex_r(n,G)$ the maximum number of edges an $r$-uniform, $G$-free hypergraph on $n$ vertices can have, and let $\lim \frac{ex_r(n,G)}{\binom nr}\...

This question is posted from StackExchange since it received no answer there. Let $f(n, e)$ be the number of triangle-free graphs on $n$ vertices and $e$ edges. From empirical evidence, I am motivated ...

My problem concerns 3-uniform hypergraphs. Let $f(n)$ be the maximal number of edges in a 3-uniform hypergraph such that no four edges form a "tetrahedron", i.e., four edges that join the ...

In a survey by Füredi and Simonovits called "The history of degenerate (bipartite) extremal graph problems," Theorem 10.5 states the following: Let $\mathcal K = K^{(r)}(a_1, \dots, a_r)$ ...

Suppose we have a graph, with multiple edges allowed. An edge-clique is a set $C$ of edges so that every two edges in $C$ share at least one endpoint. Note that any edge-clique falls into one of two ...