Related papers: Simplicial cycles and the computation of simplicia…
We analyze the time series obtained from different dynamical regimes of the logistic map by constructing their equivalent time series (TS) networks, using the visibility algorithm. The regimes analyzed include both periodic and chaotic…
In this paper, we characterize the set of spanning trees of $\mathcal{G}_{n,r}^1$ (a simple connected graph consisting of $n$ edges, containing exactly one $1$-edge-connected chain of $r$ cycles $\mathbb{C}_r^1$ and…
Polytope complexes are the generalisation of polygon meshes in geo-information systems (GIS) to arbitrary dimension, and a natural concept for accessing spatio-temporal information. Complexes of each dimension have a straight-forward…
Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze several characteristics of simple drawings of complete…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…
We introduce topological notions of polytopes and simplexes, the latter being expected to play in p-adically closed fields the role played by real simplexes in the classical results of triangulation of semi-algebraic sets over real closed…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
We define a free product of connected simple graphs that is equivalent to several existing definitions when the graphs are vertex-transitive but differs otherwise. The new definition is designed for the automorphism group of the free…
We show that every planar, 4-connected, K2;5-minor- free graph is the square of a cycle of even length at least six.
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
We define and study a simplicial complex which is a homogeneous space for the group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P. Cartier in…
Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…
Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dimensions and codimensions in such a complex, generalizing the…
Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner…
In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these…
Let $I(\Delta)^{[k]}$ denote the $k^{\text{th}}$ square-free power of the facet ideal of a simplicial complex $\Delta$ in a polynomial ring $R$. Square-free powers are intimately related to the `Matching Theory' and `Ordinary Powers'. In…
It is well known that the underlying simplicial set of any simplicial group is a Kan complex. Roughly speaking, Kan complex is an infinite-dimensional analogue of groupoid, and the relation between groupoids and categories resembles that…
The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible…