Related papers: Combinatorial constructions of intrinsic geometrie…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
In this paper we introduce a graph structure, called subspace sum graph $\mathcal{G}(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ where the vertex set is the collection of non-trivial proper subspaces of a vector space and…
Three types of geometric structure---grid triangulations, rectangular subdivisions, and orthogonal polyhedra---can each be described combinatorially by a regular labeling: an assignment of colors and orientations to the edges of an…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
When in general geometric backgrounds the metric is accompanied by torsion, the metric conformal properties should correspondingly be followed by analogous torsional conformal properties; however a combined metric torsional conformal…
We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…
We present a simplified exposition of some classical and modern results on graph drawings in the plane. These results are chosen so that they illustrate some spectacular recent higher-dimensional results on the border of topology and…
We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci…
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
This paper, following (Dymetman:1998), presents an approach to grammar description and processing based on the geometry of cancellation diagrams, a concept which plays a central role in combinatorial group theory (Lyndon-Schuppe:1977). The…
We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic dynamic graphs at the limit, when the number of nodes tends to infinity. This framework allows to preserve intrinsic geometrical information about the…
In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution,…