Related papers: Graph Theory
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…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
This is a companion piece to my paper on "Example-Based Procedural Modeling Using Graph Grammars." This paper examines some of the theoretical issues in more detail. This paper discusses some more complex parts of the implementation, why…
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…
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
A \emph{book-embedding} of a graph $G$ is an embedding of vertices of $G$ along the spine of a book, and edges of $G$ on the pages so that no two edges on the same page intersect. the minimum number of pages in which a graph can be embedded…
A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed…
The topic of this treatise is a combinatorial technique called Graph Pebbling. We investigate pebbling numbers, weight functions, flow networks, hypercubes, and the zero-sum conjecture of Erd\H{o}s and Lemke. This investigation is a…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and many coauthors). Along the way, we translate the graph theory…
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
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…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
This document aims to familiarize readers with temporal graph learning (TGL) through a concept-first approach. We have systematically presented vital concepts essential for understanding the workings of a TGL framework. In addition to…
Motivated by the remarkable interplay between (chordal) graphs and matrix algebra, we associate to each graph a so-called completion number that might encode some aspects of that interplay. We show that this number is not trivial, and we…