Given two planar graphs G_1 G 1 and G_2 G 2 that share some vertices and edges, a
simultaneous embedding with fixed edges (Sefe) is a pair of planar topological …

The splitting number of a graph G=(V, E) is the minimum number of vertex splits required to
turn G into a planar graph, where a vertex split removes a vertex v∈ V, introduces two new …

Interval graphs are intersection graphs of closed intervals of the real-line. The well-known
computational problem, called recognition, asks whether an input graph G can be …

The recently introduced problem of extending partial interval representations asks, for an
interval graph with some intervals pre-drawn by the input, whether the partial representation …

Algorithmic extension problems of partial graph representations such as planar graph
drawings or geometric intersection representations are of growing interest in topological …

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 …

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-
link representations for such graphs, in which each vertex u is represented by a geometric …

In this work we investigate the complexity of some combinatorial problems related to the
Simultaneous Embedding with Fixed Edges (SEFE) and the Partitioned T-Coherent k-Page …

A drawing concerns the process of generating geometric representations of relational
information, usually for visualization purposes. A good drawing provides an understanding …

Inspired by the increasingly popular research on extending partial graph drawings, we
propose a new perspective on the traditional and arguably most important geometric graph …