Groups of points on a straight line and plane configurations

Connectivity augmentation in plane straight line graphs

It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph by adding at most bn/2c edge...

What's in a Set of Points? (Straight Line Fitting)

Projectivities with Fixed Points on Every Line of the Plane

The system of fixed elements of a projectivity contains with any two points the line connecting them and with any two lines their intersection. It is, therefore, in its structure very much like a subplane of the plane under consideration ; and thus one may expect the structure of the projectivity to be dominated by the structure of the system of its fixed elements, provided this system is not "...

Gray Code Enumeration of Plane Straight-Line Graphs

We develop Gray code enumeration schemes for geometric straight-line graphs in the plane. The considered graph classes include plane graphs, connected plane graphs, and plane spanning trees. Previous results were restricted to the case where the underlying vertex set is in convex position.

Straight line embeddings of rooted star forests in the plane

For every 1 ≤ i ≤ n, let Ti be a rooted star with root vi, where vi is not necessary to be its center. Then the union F = T1 ∪T2 ∪ . . .∪ Tn is called a rooted star forest with roots v1, v2, . . . , vn. Let P be a set of |F | points in the plane in general position containing n specified points p1, p2, . . . , pn, where |F | denotes the order of F . Then we show that there exists a bijection φ ...