Related papers: Skolem Circles
We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
We introduce the notion of watching systems in graphs, which is a generalization of that of identifying codes. We give some basic properties of watching systems, an upper bound on the minimum size of a watching system, and results on the…
Mock threshold graphs are a simple generalization of threshold graphs that, like threshold graphs, are perfect graphs. Our main theorem is a characterization of mock threshold graphs by forbidden induced subgraphs. Other theorems…
Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions,…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Given an integer linear recurrence sequence $\langle X_n \rangle_n$, the Skolem Problem asks to determine whether there is a natural number $n$ such that $X_n = 0$. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell…
In this article we introduce the notion of weak harmonic labeling of a graph, a generalization of the concept of harmonic labeling defined recently by Benjamini et al. that allows extension to finite graphs and graphs with leaves. We…
Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly…
The main goal of this article is to introduce new quantitative characteristics of cycles in finite simple connected graphs and to establish relations of these characteristics with the stretch and spanning tree congestion of graphs. The main…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
We enumerate graph homomorphisms to quasi-complete graphs, i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels. These…
In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of…
Chordal graphs are important in algorithmic graph theory. Chordal digraphs are a digraph analogue of chordal graphs and have been a subject of active studies recently. Unlike chordal graphs, chordal digraphs lack many structural properties…
A temporal graph is a data structure, consisting of nodes and edges in which the edges are associated with time labels. To analyze the temporal graph, the first step is to find a proper graph dataset/benchmark. While many temporal graph…
Bounds on the minimum degree and on the number of vertices at- taining it have been much studied for finite edge-/vertex-minimally k- connected/k-edge-connected graphs. We give an overview of the results known for finite graphs, and show…
In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…