Related papers: RAAGedy right-angled Coxeter groups

We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs…

We customize the existing models for the bounded derived category of gentle algebras to obtain simple graph theoretic tools to analyze indecomposable objects, Auslander-Reiten triangles, and their interaction with the associated homological…

Ramsey-good graphs are graphs that contain neither a clique of size $s$ nor an independent set of size $t$. We study doubly saturated Ramsey-good graphs, defined as Ramsey-good graphs in which the addition or removal of any edge necessarily…

The author, and independently De Concini, conjectured that the monodromy of the Casimir connection of a simple Lie algebra g is described by the quantum Weyl group operators of the quantum group U_h(g). The aim of this paper, and of its…

We show that graph products of finite abelian groups are elementarily equivalent if and only if they are $\exists\forall$-equivalent if and only if they are isomorphic. In particular, two right-angled Coxeter groups are elementarily…

We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let $G$ be a group that is one-ended, hyperbolic relative to…

In this paper we study the classification of right-angled Artin groups up to commensurability. We characterise the commensurability classes of RAAGs defined by trees of diameter 4. In particular, we prove a conjecture of Behrstock and…

Let $W$ be a right-angled Coxeter group corresponding to a finite non-discrete graph $\mathcal{G}$ with at least $3$ vertices. Our main theorem says that $\mathcal{G}^c$ is connected if and only if for any infinite index quasiconvex…

Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the…

We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with…

Daligault, Rao and Thomass\'e asked whether every hereditary graph class that is well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev (JCTB 2017+) gave a negative answer to this question,…

We consider the class of finitely generated groups whose relators are powers of commutators of the generators. This class contains as a small subclass graph groups (also called RAAGs), namely if all powers are one. Graph groups are the only…

We consider problems of finding a maximum size/weight $t$-matching without forbidden subgraphs in an undirected graph $G$ with the maximum degree bounded by $t+1$, where $t$ is an integer greater than $2$. Depending on the variant forbidden…

We derive presentations of the interval groups related to all quasi-Coxeter elements in the Coxeter group of type $D_n$. Type $D_n$ is the only infinite family of finite Coxeter groups that admits proper quasi-Coxeter elements. The…

We prove that if a right-angled Artin group $A_\Gamma$ is abstractly commensurable to a group splitting non-trivially as an amalgam or HNN-extension over $\mathbb{Z}^n$, then $A_\Gamma$ must itself split non-trivially over $\mathbb{Z}^k$…

A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…

In this paper, we construct an implementable algorithm which solves the conjugacy problem in twisted right-angled Artin groups (T-RAAGs). In certain cases, the complexity is known to be linear, by reducing the problem to the twisted…

We study the right-angled Artin group action on the extension graph. We show that this action satisfies a certain finiteness property, which is a variation of a condition introduced by Delzant and Bowditch. As an application we show that…

A "biased expansion" of a graph is a kind of branched covering graph with additional structure related to combinatorial homotopy of circles. Some but not all biased expansions are constructed from groups ("group expansions"); these include…

We compute the group homology, the algebraic $K$- and $L$-groups, and the topological $K$-groups of right-angled Artin groups, right-angled Coxeter groups, and more generally, graph products.