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Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…
We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…
We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…
The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of…
Given any directed graph E one can construct a graph inverse semigroup G(E), where, roughly speaking, elements correspond to paths in the graph. In this paper we study the semigroup-theoretic structure of G(E). Specifically, we describe the…
We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.
A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…
Motivated in part by combinatorial applications to certain sum-product phenomena, we introduce unimodular graphs over finite fields and, more generally, over finite valuation rings. We compute the spectrum of the unimodular graphs, by using…
Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
Tangle-tree theorems are an important tool in structural graph theory, and abstract separation systems are a very general setting in which tangle-tree theorems can still be formulated and proven. For infinite abstract separation systems, so…
The Known Menger's theorem states that in a finite graph, the size of a minimum separator set of any pair of vertices is equal to the maximum number of disjoint paths that can be found between these two vertices. In this paper, we study the…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…
Polytopes from subgraph statistics are important in applications and conjectures and theorems in extremal graph theory can be stated as properties of them. We have studied them with a view towards applications by inscribing large explicit…
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 introduce the notion of colorful minors, which generalizes the classical concept of rooted minors in graphs. A $q$-colorful graph is defined as a pair $(G, \chi),$ where $G$ is a graph and $\chi$ assigns to each vertex a (possibly empty)…
Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…