Related papers: Graphs Embedded into Finite Projective Planes
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
We generalize the idea of cofinite groups, due to B. Hartley. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions. The idea of constructing a cofinite graph starts…
We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…
Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhombus. We give a necessary and sufficient condition for the…
Work of Glover and Huneke shows that a cubic graph embeds into the real projective plane if and only if it does not contain one of six topological minors called cubic projective plane obstructions. Here we classify up to equivalence the…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
We will determine all infinite $2$-locally finite groups as well as infinite $2$-groups with planar subgroup graph and show that infinite groups satisfying the chain conditions containing an involution do not have planar embeddings. Also,…
Graph embedding is the major technique which is used to map guest graph into host graph. In architecture simulation, graph embedding is said to be one of the strongest application for the execution of parallel algorithm and simulation of…
In this paper, we present a constructive and proof-relevant development of graph theory, including the notion of maps, their faces, and maps of graphs embedded in the sphere, in homotopy type theory. This allows us to provide an elementary…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
We prove that if a unimodular random graph is almost surely planar and has finite expected degree, then it has a combinatorial embedding into the plane which is also unimodular. This implies the claim in the title immediately by a theorem…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…
Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
Traditional representations of graphs and their duals suggest the requirement that the dual vertices be placed inside their corresponding primal faces, and the edges of the dual graph cross only their corresponding primal edges. We consider…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…