For a set $ P $ of $ n $ points in the plane in general position, a non-crossing spanning tree
is a spanning tree of the points where every edge is a straight-line segment between a pair …

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 …

In this paper we investigate the structure of flip graphs on non-crossing perfect matchings in
the plane. Specifically, consider all non-crossing straight-line perfect matchings on a set of 2 …

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 …

Two plane drawings of 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. Let S be a convex point set of …

For a simple drawing D of the complete graph K n, two (plane) subdrawings are compatible
if their union is plane. Let TD be the set of all plane spanning trees on D and F (TD) be the …

A perfect straight-line matching $ M $ on a finite set $ P $ of points in the plane is a set of
segments such that each point in $ P $ is an endpoint of exactly one segment. $ M $ is non …

This column is devoted to the memory of Ferran Hurtado who unexpectedly passed away in
2014. In writing this column we remember some of the problems that he posed or liked. From …

A geometric graph is a graph whose vertex set is a set of points in the plane and whose
edge set contains straight-line segments. A matching in a graph is a subset of edges of the …