Suppose that we are given in the plane a set of $n$ points, $P$, and $m$ topological trees that pairwise intersect exactly once such that each leaf of each tree is from $P$.
Is it true that $m\le n$?
Note that if each tree consists of a single edge, then we get back the original thrackle conjecture.
The question was originally posed in this paper; it also appeared on the Emléktábla workshop.
