Related papers: Characterizing Planar Graphs
A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their…
In this paper, we investigate the use of an unsupervised label clustering technique and demonstrate that it enables substantial improvements in visual relationship prediction accuracy on the Person in Context (PIC) dataset. We propose to…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
Monocular depth estimation is a highly challenging problem that is often addressed with deep neural networks. While these are able to use recognition of image features to predict reasonably looking depth maps the result often has low metric…
The digital conversion of information stored in documents is a great source of knowledge. In contrast to the documents text, the conversion of the embedded documents graphics, such as charts and plots, has been much less explored. We…
Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
This paper provides an introduction to trace diagrams at a level suitable for advanced undergraduates. Trace diagrams are a non-traditional notation for linear algebra. Vectors are represented by edges in a diagram, and matrices by markings…
Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general…
Architecture styles characterise families of architectures sharing common characteristics. We have recently proposed configuration logics for architecture style specification. In this paper, we study a graphical notation to enhance…
The present work continues the program of summing planar Feynman graphs on the world sheet. Although it is based on the same classical action introduced in the earlier work, there are important new features: Instead of the path integral…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…
Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a…
Graph classification is an important problem with applications across many domains, like chemistry and bioinformatics, for which graph neural networks (GNNs) have been state-of-the-art (SOTA) methods. GNNs are designed to learn node-level…
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…