Two graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ admit a geometric simultaneous
embedding if there exists a set of points P and a bijection M: P -> V that
induce planar straight-line embeddings both for $G_1$ and for $G_2$. While it
is known that two caterpillars always admit a geometric simultaneous embedding
and that two trees not always admit one, the question about a tree and a path
is still open and is often regarded as the most prominent open problem in this
area.