@inproceedings{15082,
  abstract     = {Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2.
We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter
of this graph is either 4 or 5, independent of n.},
  author       = {Aichholzer, Oswin and Obmann, Julia and Patak, Pavel and Perz, Daniel and Tkadlec, Josef},
  booktitle    = {36th European Workshop on Computational Geometry},
  location     = {Würzburg, Germany, Virtual},
  title        = {{Disjoint tree-compatible plane perfect matchings}},
  year         = {2020},
}