The crossing number is a popular tool in graph drawing and visualization, but there is not
really just one crossing number; there is a large family of crossing number notions of which …

In this survey/introductory article, we first present the basics of the field of Parameterized
Complexity, made accessible to readers without background on the subject. Afterwards, we …

A drawing of an (undirected) graph G is a map** φ that assigns to each vertex a distinct
point in the plane and to each edge uw a continuous curve φ (uυ) in the plane from φ (η) to φ …

Beyond-planar graph classes are usually defined via forbidden configurations or patterns in
a drawing. In this paper, we formalize these concepts on a combinatorial level and show …

We propose a new conjecture on hardness of low-degree $2 $-CSP's, and show that new
hardness of approximation results for Densest $ k $-Subgraph and several other problems …

Let $ G $ be a connected planar (but not yet embedded) graph and $ F $ a set of edges with
ends in $ V (G) $ and not belonging to $ E (G) $. The multiple edge insertion problem (MEI) …

For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its
incident edges, represented by the labels of their other endpoints. The extended rotation …

The crossing number of a graph $ G $ is the minimum number of crossings in a drawing of $
G $ in the plane. A rectilinear drawing of a graph $ G $ represents vertices of $ G $ by a set …

We propose a new conjecture on hardness of 2-CSP's, and show that new hardness of
approximation results for Densest k-Subgraph and several other problems, including a …

The basic crossing number problem is to determine the minimum number of crossings in a
topological drawing of an input graph in the plane. In this paper, we develop fixed-parameter …