We consider the following question: How many edge-disjoint plane spanning
trees are contained in a complete geometric graph GKn on any set S of n
points in general position in the plane? We show that this number is in
Ω(n). Further, we consider variants of this problem by bounding
the diameter and the degree of the trees (in particular considering spanning
paths).Comment: This work was presented at the 26th Canadian Conference on
Computational Geometry (CCCG 2014), Halifax, Nova Scotia, Canada, 2014. The
journal version appeared in Information Processing Letters, 124 (2017),
35--4