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One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…

An introductory paper to the graph k-colorability problem.

A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations…

Reducing a graph while preserving its overall properties is an important problem with many applications. Typically, reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no…

We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…

While a plethora of research has been devoted to extoling the power and importance of data visualization, research on the effectiveness of data visualization methods from a human perceptual, and more generally, a cognitive standpoint…

We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.

An approach of using RGB-tilings for proving the Four Color Theorem discussed in three previous work is expanded in this paper. A novel methodology and revisions for the methodology in the three aforementioned papers are discussed, and a…

In this paper, we introduce a graph coloring game called the Edge-Distinguishing Game (EDGe). The edge-distinguishing chromatic number of a graph is used to determine the moves each player can make. We determine which player has a winning…

In this paper we provide a comprehensive introduction to knowledge graphs, which have recently garnered significant attention from both industry and academia in scenarios that require exploiting diverse, dynamic, large-scale collections of…

In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach…

Graph learning models have demonstrated great prowess in learning expressive representations from large-scale graph data in a wide variety of real-world scenarios. As a prevalent strategy for training powerful graph learning models, the…

A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which can be distinguished using 2 colors. The cost $\rho(G)$ of a…

Despite the existence of numerous colorization methods, several limitations still exist, such as lack of user interaction, inflexibility in local colorization, unnatural color rendering, insufficient color variation, and color overflow. To…

The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires…

The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…

The list coloring problem is a variant of vertex coloring where a vertex may be colored only a color from a prescribed set. Several applications of vertex coloring are more appropriately modelled as instances of list coloring and thus we…

I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…

This paper introduces a novel method for image colorization that utilizes a color transformer and generative adversarial networks (GANs) to address the challenge of generating visually appealing colorized images. Conventional approaches…

Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of…