We survey the complexity class $\exists\mathbb {R} $, which captures the complexity of
deciding the existential theory of the reals. The class $\exists\mathbb {R} $ has roots in two …

In a Lombardi drawing of a graph the vertices are drawn as points and the edges are drawn
as circular arcs connecting their respective endpoints. Additionally, all vertices have perfect …

We prove that the following problem is complete for the existential theory of the reals: Given
a planar graph and a polygonal region, with some vertices of the graph assigned to points …

Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line
segment. Given a planar graph G, the segment number of G is the minimum number of …

The of a planar graph G is the smallest number of line segments needed for a planar straight-
line drawing of G. Dujmović, Eppstein, Suderman, and Wood [CGTA'07] introduced this …

In this thesis, we explore a young branch of computational complexity that deals with
problems whose solutions consist of real numbers subject to a given set of polynomial …

It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb {R}^
3$ and that any planar graph admits the same even in $\mathbb {R}^ 2$. For a graph $ G …

An arrangement of a set of non-self-intersecting curves is their embedding in the Euclidean
plane such that at each intersection point the curves involved cross each other …

Graph Drawing is a field of research that has application in any field of science that needs to
visualize binary relations. This thesis covers various problems arising when drawing graphs …

A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple)
pseudoline arrangement. We study the corresponding graph realization problem and …