Related papers: Configuration Spaces of Colored Graphs
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this…
Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global…
The notion of $\textbf{Gray}$-category, a semi-strict $3$-category in which the middle four interchange is weakened to an isomorphism, is central in the study of three-dimensional category theory. In this context it is common practice to…
In this paper we consider the generalized anchored configuration spaces on $n$ labeled points on a~graph. These are the spaces of all configurations of $n$ points on a~fixed graph $G$, subject to the condition that at least $q$ vertices in…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
Cographs--defined most simply as complete graphs with colored lines--both dualize and generalize ordinary graphs, and promise a comparably wide range of applications. This article introduces them by examples, catalogues, and elementary…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
Motivated by the work in [15], this paper deals with the theory of the braids from chromatic configuration spaces. This kind of braids possess the property that some strings of each braid may intersect together and can also be untangled, so…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.