Discrete geometry on colored point sets in the plane has a long history, but this research
area has been extensively developed in the last 2 decades. In 2003, a short survey entitled …

We consider matchings with diametral disks between two sets of points R and B. More
precisely, for each pair of matched points p∈ R and q∈ B, we consider the disk through p …

Abstract Huemer et al.(Discrete Mathematics, 2019) proved that for any two point sets R and
B with| R|=| B|, the perfect matching that matches points of R with points of B, and maximizes …

The operation of transforming one spanning tree into another by replacing an edge has
been considered widely, both for general and planar straight-line graphs. For the latter …

We study an old geometric optimization problem in the plane. Given a perfect matching M on
a set of n points in the plane, we can transform it to a non-crossing perfect matching by a …

Let $\mathcal {P} $ be a set of $ n= 2m+ 1$ points in the plane in general position. We define
the graph $ GM_\mathcal {P} $ whose vertex set is the set of all plane matchings on …

Let $ X_ {2k} $ be a set of $2 k $ labeled points in convex position in the plane. We consider
geometric non-intersecting straight-line perfect matchings of $ X_ {2k} $. Two such …

Given n red and n blue points in general position in the plane, it is well-known that there is a
perfect matching formed by non-crossing line segments. We characterize the bichromatic …

Abstract Let P= B∪ R be a set of 2n points in general position in the plane, where B is a set
of n blue points and R a set of n red points. A BR-matching is a plane geometric perfect …

Given a set P of n points in the plane, where n is even, we consider the following question:
How many plane perfect matchings can be packed into P? For points in general position we …