Related papers: Matching groups and gliding systems
We show that each perfect matching in a bipartite graph $G$ intersects at least half of the perfect matchings in $G$. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of…
The aim of this paper is to investigate the homology groups of mathematical models of concurrency. We study the Baues-Wirsching homology groups of a small category associated with a partial monoid action on a set. We prove that these groups…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
We say that a group G is a cube group if it is generated by a set S of involutions such that the corresponding Cayley graph Cay(G,S) is isomorphic to a cube. Equivalently, G is a cube group if it acts on a cube such that the action is…
Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
We consider a matching problem in a bipartite graph $G$ where every vertex has a capacity and a strict preference order on its neighbors. Furthermore, there is a cost function on the edge set. We assume $G$ admits a perfect matching, i.e.,…
I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
This paper introduces gluing diagrams a combinatorial tool to construct homomorphisms between the shift pseudogroups of directed graphs and thus also their full groups of shifts. We will establish which of these diagrams produce…
The Jacobian group of a graph is a finite abelian group through which we can study the graph in an algebraic way. When the graph is a finite abelian covering of another graph, the Jacobian group is equipped with the action of the Galois…
Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…
In a 2018 paper, Cameron and Semeraro posed the problem of finding all group-graph reciprocal pairs. In this paper, we make a significant contribution to finding all such pairs. A group and graph form a reciprocal pair if they satisfy the…
We consider a generalization of group testing where the potentially contaminated sets are the members of a given hypergraph ${\cal F}=(V,E)$. This generalization finds application in contexts where contaminations can be conditioned by some…
In this paper, all finite groups whose commuting (non-commuting) graphs can be embed on the plane, torus or projective plane are classified.
Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
In this paper, we investigate certain graphs defined on groups, with a focus on infinite groups. The graphs discussed are the power graph, the enhanced power graph, and the commuting graph whose vertex set is a group $G$. The power graph is…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…