Related papers: A note on the structure of expanders
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
In this paper, we study the large-scale structure of dense regular graphs. This involves the notion of robust expansion, a recent concept which has already been used successfully to settle several longstanding problems. Roughly speaking, a…
This paper presents a possible link between Cages and Expander Graphs by introducing three interconnected variants of the Bermond and Bollob\'as Conjecture, originally formulated in 1981 within the context of the Degree/Diameter Problem. We…
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…
This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $\Omega(|A|^{3/2})$ three-term arithmetic progressions.
This note is the follow up to a paper by M. Waldschmidt.
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
In this paper, we give a class of reconstructible graphs.
On the simultaneous edge coloring of graphs
This is an investigation of the role of shuffling and concatenating in the theory of graph drawing. A simple syntactic description of these and related operations is proved complete in the context of finite partial orders, as general as…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(\textbf{r}, \textbf{d})$ on $G$, we describe a construction which associates to it a graph $G'$ on $n-1$…
The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
In this brief note I try to give a simple example of where physical intuition about a collection of interacting qubits can lead to the construction of "natural" versions of what are, generically, quite abstract mathematical objects - in…
The edge expansion of a graph is the minimum quotient of the number of edges in a cut and the size of the smaller one among the two node sets separated by the cut. Bounding the edge expansion from below is important for bounding the…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We…