Related papers: Coreo-Graph: un progetto di teoria dei grafi e dan…
People typically consider only European mathematics as orthodox, often intentionally or unintentionally overlooking the existence of mathematics from non-European societies. Inspired by Maria Ascher's two well-known papers on sand drawings…
Teaching graph theory with the most adequate tools requires time and ideas. We present how an open community of teachers shares contents and ideas on an innovative platform. The objective is to get the students autonomous in their training…
An Eulerian walk (or Eulerian trail) is a walk (resp. trail) that visits every edge of a graph $G$ at least (resp. exactly) once. This notion was first discussed by Leonhard Euler while solving the famous Seven Bridges of K\"{o}nigsberg…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
Continual learning on graph data has recently attracted paramount attention for its aim to resolve the catastrophic forgetting problem on existing tasks while adapting the sequentially updated model to newly emerged graph tasks. While there…
Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…
We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory,…
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks…
This is a graduate-level introduction to graph theory, corresponding to a quarter-long course. It covers simple graphs, multigraphs as well as their directed analogues, and more restrictive classes such as tournaments, trees and…
The presented work focuses on problems from determinant theory, set theory and topology. The term graph is the binding element that connects these problems. Graphs are distinguished by their geometrical simplicity, which helps in showing…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
Dancing in a duet often requires a heightened attunement to one's partner: their orientation in space, their momentum, and the forces they exert on you. Dance artists who work in partnered settings might have a strong embodied understanding…
Deep neural networks for graphs have emerged as a powerful tool for learning on complex non-euclidean data, which is becoming increasingly common for a variety of different applications. Yet, although their potential has been widely…
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…
The Erd\H{o}s, Gr\"unwald, and Weiszfeld theorem is a characterization of those infinite graphs which are Eulerian. That is, infinite graphs that admit infinite Eulerian paths. In this article we prove an effective version of the Erd\H{o}s,…
Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the…
The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to…
Leonhard Euler was working for the St. Petersburg Academy of Sciences (Russia) and Prussian Academy of Sciences during various periods of his life. It is not a popular knowledge about Euler's contacts with Polish scientists of his era and…