Related papers: Drawing maps on oriented surfaces

We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…

In this paper, we present a constructive and proof-relevant development of graph theory, including the notion of maps, their faces, and maps of graphs embedded in the sphere, in homotopy type theory. This allows us to provide an elementary…

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…

In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.

We present an algorithm to support the dynamic embedding in the plane of a dynamic graph. An edge can be inserted across a face between two vertices on the face boundary (we call such a vertex pair linkable), and edges can be deleted. The…

A k-outerplanar graph is a graph that can be drawn in the plane without crossing such that after k-fold removal of the vertices on the outer-face there are no vertices left. In this paper, we study how to triangulate a k-outerplanar graph…

Using programmable network devices to aid in-network machine learning has been the focus of significant research. However, most of the research was of a limited scope, providing a proof of concept or describing a closed-source algorithm. To…

We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.

In this paper we fully describe all tropical linear mappings in the tropical projective plane, that is, maps from the tropical plane to itself given by tropical multiplication by an order 3 matrix. An erratum has been added fixing two…

We study straight-line drawings of planar graphs with prescribed face areas. A plane graph is 'area-universal' if for every area assignment on the inner faces, there exists a straight-line drawing realizing the prescribed areas. For…

Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…

A Schnyder wood is an orientation and coloring of the edges of a planar map satisfying a simple local property. We propose a generalization of Schnyder woods to graphs embedded on the torus with application to graph drawing. We prove…

A convex combination mapping of a planar graph is a plane mapping in which the external vertices are mapped to the corners of a convex polygon and every internal vertex is a proper weighted average of its neighbours. If a planar graph is…

Automated proof assistants are a technology pre-empting mistakes in mathematics. In our practice we have seen that reasoning about planar diagrams is difficult to both humans and computers. One example that has led to wrong statements in…

Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…

A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we present a bijective link between unicellular maps on a non-orientable surface and…

This paper presents a novel algorithmic framework for the computational design, simulation, and fabrication of a hexagonal grid-based double-curvature structure with planar hexagonal panels. The journey begins with constructing a robust…