The ACO Seminar (2011-2012)

Let $\cal F$ be a family of $k$-graphs. The \emph{Tur\'an function $ex(n,F)$} is the maximum number of edges in an $\cal F$-free $k$-graph on $n$ vertices. The \emph{Tur\'an density $\pi(\cal F)$} is the limit of $ex(n,F)/{n\choose k}$ as $n$ tends to infinity. (The limit is known to exists for every $\cal F$.)

We disprove the conjecture of Chung and Graham that $\pi(\cal F)$ is rational for every finite family $\cal F$.