A

Suppose that we are given a forest *F* of *k* rooted trees
*T_1,...,T_k*, a set of *n* points in the plane that are in general
position, and an ordered subset *p_1,...,p_k* of these points.

**Problem:** *Can we find a geometric realization of* F with
no crossing edges such that the root of T_i *is at point* p_i.

Kaneko and Kano [KK1,KK2,KK3] have found such realizations in some special
cases, including *a) k = 2, b)* each tree is a star, and *c)*
all of the trees are of the same size. However, they conjecture that the
problem is false in general.

**References:**

[KK1] A. Kaneko and M. Kano, Straight-line embeddings of two rooted trees in the plane, preprint.

[KK2] A. Kaneko and M. Kano, Straight-line embeddings of rooted star forests in the plane, preprint.

[KK1] A. Kaneko and M. Kano, A balanced partition of points in the plane
and tree embedding problems, preprint.

Send comments to *dan.archdeacon@uvm.edu*

December 2003