Related papers: Canonical graph decompositions via coverings
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We show that finitely presented groups which admit $k$-planar Cayley graphs contain finite-index subgroups with planar Cayley graphs. More generally, we answer a question of Georgakopoulos and Papasoglu in the special case of coarsely…
We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a…
We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…
The path spaces of a directed graph play an important role in the study of graph $\css$. These are topological spaces that were originally constructed using groupoid and inverse semigroup techniques. In this paper, we develop a simple,…
We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs and matroids, but can be much more general or quite different. The theorem asserts a duality…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…
We study the free product of rooted graphs and its various decompositions using quantum probabilistic methods. We show that the free product of rooted graphs is canonically associated with free independence, which completes the proof of the…
We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product…
The present work describes the asymptotic local shape of a graph drawn uniformly at random from all connected simple planar graphs with n labelled vertices. We establish a novel uniform infinite planar graph (UIPG) as quenched limit in the…
In this paper we employ Tutte's theory of bridges to derive a decomposition theorem for binary matroids arising from signed graphs. The proposed decomposition differs from previous decomposition results on matroids that have appeared in the…
We explore properties of generalized Paley graphs and we extend a result of Lim and Praeger by providing a more precise description of the connected components of disconnected generalized Paley graphs. This result leads to a new…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…
We show that if a subset $\Psi$ of the ends of a graph $G$ can be displayed by a tree-decomposition of finite adhesion, then it can also be displayed by a linked such tree-decomposition. This tree-decomposition captures all combinatorial…
The method for calculation of the canonical decomposition that approximates a tensor of high order is considered, which requires moderate computational resources. It is based on the replacement of the approximation error norm (global…