Related papers: A Note on "Regularity lemma for distal structures"
We present a new semidefinite Farkas lemma involving a side constraint on the rank. This lemma is then used to present a new proof of a recent characterization, by Connelly and Gortler, of dimensional rigidity of bar frameworks.
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
In the literature, the notion of discrepancy is used in several contexts, even in the theory of graphs. Here, for a graph $G$, $\{-1, 1\}$ labels are assigned to the edges, and we consider a family $\mathcal{S}_G$ of (spanning) subgraphs of…
We characterise the form of all simple, finite graphs for which the girth of the graph is equal to the circumference of the graph. We apply this to prove a bound on the number of edges in such a graph.
Let $D$ be a strongly connected digraph. The average distance $\bar{\sigma}(v)$ of a vertex $v$ of $D$ is the arithmetic mean of the distances from $v$ to all other vertices of $D$. The remoteness $\rho(D)$ and proximity $\pi(D)$ of $D$ are…
Duval, in "A Directed Graph Version of Strongly Regular Graphs" [{\it Journal of Combinatorial Theory}, Series A 47 (1988) 71 - 100], introduced the concept of directed strongly regular graphs. In this paper we construct several rich…
The analysis of large simple graphs with extreme values of the densities of edges and triangles has been extended to the statistical structure of typical graphs of fixed intermediate densities, by the use of large deviations of Erdoes-Renyi…
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…
We observe that the nonstandard finite cardinality of a definable set in a strongly minimal pseudofinite structure D is a polynomial over the integers in the nonstandard finite cardinality of D. We conclude that D is unimodular, hence also…
We prove a regularity lemma with respect to arbitrary Keisler measures mu on V, nu on W where the bipartite graph (V,W,R) is definable in a saturated structure M and the formula R(x,y) is stable. The proof is rather quick and uses local…
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…
Let $F$ and $G$ be simple finite undirected graphs. A graph $G$ is called $F$-irregular if any two of its distinct vertices belong to different numbers of copies of $F$ in $G$. According to the strong conjecture about $F$-irregular graphs…
We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.
In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multiplicative ideal theory and the graph theoretic structure of…
We introduce Schottky maps-conformal maps between relative Schottky sets, and study their local rigidity properties. This continues the investigations of relative Schottky sets initiated in [S. Merenkov, "Planar relative Schottky sets and…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of…
An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical'…
The concept of directed strongly regular graphs was introduced by Duval in his paper, A Directed Graph Version of Strongly Regular Graphs. Duval also provided several construction methods for directed strongly regular graphs. The directed…
In this work, which was inspired by the article [2] by M. V. Velasco and A. R. Villena, we obtain a characterization for probably continuous operators and show that the probability of a linear random operator being continuous coincides with…