Related papers: Cartesian product of hypergraphs: properties and a…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical…
Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex is either alone in its color class or adjacent to all vertices of at least one color class. A dominated coloring of a graph is a proper coloring…
Products in double categories, as found in cartesian double categories, are an elegant concept with numerous applications, yet also have a few puzzling aspects. In this paper, we revisit double-categorical products from an unbiased…
In this paper, we focus on learning the underlying product graph structure from multidomain training data. We assume that the product graph is formed from a Cartesian graph product of two smaller factor graphs. We then pose the product…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
In the past couple of years a rich connection has been found between the fields of descriptive set theory and distributed computing. Frequently, and less surprisingly, finitary algorithms can be adopted to the infinite setting, resulting in…
There are many variations on partition functions for graph homomorphisms or colorings. The case considered here is a counting or hard constraint problem in which the range or color graph carries a free and vertex transitive Abelian group…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can…
Deep generative models have recently made a remarkable progress in capturing complex probability distributions over graphs. However, they are intractable and thus unable to answer even the most basic probabilistic inference queries without…
In this paper we investigate the connectedness and the isomorphism problems for zig-zag products of two graphs. A sufficient condition for the zig-zag product of two graphs to be connected is provided, reducing to the study of the…
The families of graphs defined by a certain type of system of equations over commutative rings have been studied and used since 1990s. This survey presents these families and their applications related to graphs, digraphs, and hypergraphs.…
To each finite frame $\varphi$ in an inner product space $\mathcal{H}$ we associate a simple graph $G(\varphi)$, called {\it frame graph}, with the vectors of the frame as vertices and there is an edge between vertices $f$ and $g$ provided…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
In a recent paper Cameron, Lakshmanan and Ajith began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable…
Gaussian periods are certain sums of roots of unity whose study dates back to Gauss's seminal work in algebra and number theory. Recently, large scale plots of Gaussian periods have been revealed to exhibit striking visual patterns, some of…