Related papers: Drawing Diestel-Leader graphs in 3D
A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our…
We exhibit an explicit list of nine graphs such that a graph drawn in the Klein bottle is 5-colorable if and only if it has no subgraph isomorphic to a member of the list.
A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction…
We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…
Generating bitmap graphics from text has gained considerable attention, yet for scientific figures, vector graphics are often preferred. Given that vector graphics are typically encoded using low-level graphics primitives, generating them…
The k-th power D^k of a directed graph D is defined to be the directed graph on the vertices of D with an arc from a to b in D^k iff one can get from a to b in D with exactly k steps. This notion is equivalent to the k-fold composition of…
A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex has a list of at least k available colors and vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance…
This paper describes a general method for representing $k$-token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and Johnson graphs as lift graphs on cyclic groups. As an…
In this paper is clarify the summaries codes for programmers through three-dimensional shapes, and clearly programmers and developers, scholars and researchers in the field of software engineering, as well as researchers from the…
The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism. In this paper, we investigate…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Visualization of multidimensional, categorical data is a common challenge across scientific areas and, in particular, the life sciences. The goal is to create a comprehensive overview of the underlying data which allows to assess multiple…
Contact representations of graphs have a long history. Most research has focused on problems in 2D, but 3D contact representations have also been investigated, mostly concerning fully-dimensional geometric objects such as spheres or cubes.…
In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side…
For given a graph $H$, a graphic sequence $\pi=(d_1,d_2,...,d_n)$ is said to be potentially $H$-graphic if there exists a realization of $\pi$ containing $H$ as a subgraph. In this paper, we characterize the potentially $H$-graphic…
The general position number for graphs ask for largest vertex subsets $S$ such that no three vertices are contained on a common shortest path. We examine this problem in the setting of directed graphs. We provide bounds for the general…
This paper provides a linear time algorithm in the number of edges that, given a simple 3-connected non-planar graph G with a Klein bottle rotation system, outputs a straight line drawing of G with no crossings on the flat Klein bottle.
In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised…
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general…
These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.