Graph theory is a fundamental branch of mathematics that examines networks composed of
nodes (vertices) and connections (edges). This paper explores the concepts of permutation …

A contact representation by triangles of a graph is a set of triangles in the plane such that
two triangles intersect on at most one point, each triangle represents a vertex of the graph …

We prove that every planar graph has a representation using axis-parallel cubes in three
dimensions in such a way that there is a cube corresponding to each vertex of the planar …

In this paper we study connections between planar graphs, Schnyder woods, and
orthogonal surfaces. Schnyder woods and the face counting approach have important …

We study contact representations of non-planar graphs in which vertices are represented by
axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries …

We study contact representations for planar graphs, with vertices represented by simple
polygons and adjacencies represented by point-contacts or side-contacts between the …

We consider contact representations of graphs where vertices are represented by cuboids,
ie interior-disjoint axis-aligned boxes in 3D space. Edges are represented by a proper …

It implicitly follows from the work of [Colbourn, El-Mallah: On two dual classes of planar
graphs. Discrete Mathematics 80 (1): 21-40 (1990)] that every planar partial 3-tree is a …

We study representations of graphs by contacts of circular arcs, CCA-representations for
short, where the vertices are interior-disjoint circular arcs in the plane and each edge is …

We study balanced circle packings and circle-contact representations for planar graphs,
where the ratio of the largest circle's diameter to the smallest circle's diameter is polynomial …