Disjoint tree-compatible plane perfect matchings

Oswin Aichholzer, Julia Obmann, Pavel Paták, Daniel Perz, Josef Tkadlec

Research output: Contribution to conferencePaperpeer-review


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.
Original languageEnglish
Publication statusPublished - 2020
Event36th European Workshop on Computational Geometry - University of Würzburg, Virtuell, Germany
Duration: 16 Mar 202018 Mar 2020


Conference36th European Workshop on Computational Geometry
Abbreviated titleEuroCG 2020
Internet address


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