For a set P of n points in general position in the plane, the flip graph F (P) has a vertex for
each noncrossing spanning tree on P and an edge between any two spanning trees that can …

Flip graphs of non-crossing configurations in the plane are widely studied objects, eg, flip
graph of triangulations, spanning trees, Hamiltonian cycles, and perfect matchings …

A non-crossing spanning tree of a set of points in the plane is a spanning tree whose edges
pairwise do not cross. Avis and Fukuda in 1996 proved that there always exists a flip …

A (multi) set of segments in the plane may form a TSP tour, a matching, a tree, or any
multigraph. If two segments cross, then we can reduce the total length with the following flip …

A set of n segments in the plane may form a Euclidean TSP tour, a tree, or a matching,
among others. Optimal TSP tours as well as minimum spanning trees and perfect matchings …

Given a finite set $ S $ of points, we consider the following reconfiguration graph. The
vertices are the plane spanning paths of $ S $ and there is an edge between two vertices if …

How can we reconfigure a given set of n segments with fixed endpoints in the plane into a
crossing-free set? We remove a pair of crossing segments and insert one of the two pairs of …

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 …