相关论文: Extending Graph Burning to Hypergraphs

Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. Over the years, graph learning has transcended from graph theory to graph data mining. With the…

Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…

The semi-random hypergraph process is a natural generalisation of the semi-random graph process, which can be thought of as a one player game. For fixed $r < s$, starting with an empty hypergraph on $n$ vertices, in each round a set of $r$…

Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…

Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…

In this paper we study the graph parameter of burning number, introduced by Bonato, Janssen, and Roshanbin (2014). We are particular interested in determining the burning number of Circulant graphs. In this paper, we find upper and lower…

Brushing of graphs is a graph searching process in which the searching agents are called brushes. We focus on brushing directed graphs based on a new model in which the brushes can only travel in the same direction as the orientation of the…

We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…

Given a graph $G=(V, E)$, the problem of Graph Burning is to find a sequence of nodes from $V$, called a burning sequence, to burn the whole graph. This is a discrete-step process, and at each step, an unburned vertex is selected as an…

Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…

Motivated by the burning and cooling processes, the burning game is introduced. The game is played on a graph $G$ by the two players (Burner and Staller) that take turns selecting vertices of $G$ to burn; as in the burning process, burning…

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,…

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…

Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations. Aim of this survey is to describe the main research…

Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…

Edge bundling is an important concept heavily used for graph visualization purposes. To enable the comparison with other established near-planarity models in graph drawing, we formulate a new edge-bundling model which is inspired by the…

This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and…

A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the…