Related papers: A sequence of triangle-free pseudorandom graphs
The Alon-Tarsi number of a polynomial is a parameter related to the exponents of its monomials. For graphs, their Alon-Tarsi number is the Alon-Tarsi number of their graph polynomials. As such, it provides an upper bound on their choice and…
This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small…
Pseudo-random arrays and perfect maps are the two-dimensional analogs of M-sequences and de Bruijn sequences, respectively. We modify the definitions to be applied to codes. These codes are also the two-dimensional analogs of certain…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
We explain how massive instances of scale-free graphs following the Barabasi-Albert model can be generated very quickly in an embarrassingly parallel way. This makes this popular model available for studying big data graph problems. As a…
We find a strong separation between two natural families of simple rank one theories in Keisler's order: the theories $T_\mathfrak{m}$ reflecting graph sequences, which witness that Keisler's order has the maximum number of classes, and the…
We present some results on the structure of line graphs of triangle-free graphs and a homogenization of the line graph of the universal homogeneous triangle-free graph in a finite relational language with arity 4. This result is relevant to…
The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of…
A Delaunay graph built on a planar point set has an edge between two vertices when there exists a disk with the two vertices on its boundary and no vertices in its interior. When the disk is replaced with an equilateral triangle, the…
We prove that the random ordered graph is a semi-retract of the canonically ordered atomless Boolean algebra, hereby answering an open question of Barto\v{s}ov\'a and Scow.
The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…
We present a simple mechanism, which can be randomised, for constructing sparse $3$-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over $\mathbb{Z}_2^t$ and have vertex degree…
The paper provides the first constructions of strongly regular graphs and association schemes from weakly regular plateaued functions over finite fields of odd characteristic. We generalize the construction method of strongly regular graphs…
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…
We propose a class of networks which can be regarded as an extension of the graphitic network. These networks are constructed so that surface states with non-bonding character (edge states) are formed in a tight-binding model with one…
In this paper, we construct the Bessel line ensemble, a countable collection of continuous random curves. This line ensemble is stationary under horizontal shifts with the Bessel point process as its one-time marginal. Its finite…
Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of…
The problem of determining the maximum number of edges in an $n$-vertex graph that does not contain a 4-cycle has a rich history in extremal graph theory. Using Sidon sets constructed by Bose and Chowla, for each odd prime power $q$ we…
This paper presents the development of a new class of algorithms that accurately implement the preferential attachment mechanism of the Barab\'asi-Albert (BA) model to generate scale-free graphs. Contrary to existing approximate…
A general construction of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic and this construction, several classes of binary sequences with optimal autocorrelation and other…