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We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the ...
With the aim of extending the coverage and improving the performance of impulse radio ultra-wideband (UWB) systems, this paper focuses on developing a novel single differential encoded decode and forward (DF) non-cooperative relaying scheme (NCR). To favor ...
Modern data processing tasks frequently involve structured data, for example signals defined on the vertex set of a weighted graph. In this paper, we address the problem of inference of mobility patterns from data defined on geographical graphs based on sp ...
A graph drawn in the plane is called k-quasi-planar if it does not contain k pair-wise crossing edges. It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best k ...
We analyze the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...
We consider graphs that admit polyline drawings where all crossings occur at the same angle alpha is an element of (0, pi/2]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This r ...
A faithful (unit) distance graph in R-d is a graph whose set of vertices is a finite subset of the d-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is exactly 1. A (unit) distance graph in Rd ...
In this note we present a method to compute approximate descriptions of a class of stochastic systems. For the method to apply, the system must be presented as a Markov chain on a state space consisting in graphs or graph-like objects, and jumps must be de ...
Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...
The social and economical impact a virus has in a population is not negligible. For this reason, gaining a theoretical understanding of the behavior of a virus is of prime importance. This project is going to be divided in several parts. First, we will dis ...
