Community structure in graph-modeled data appears in a range of disciplines that comprise network science. Its importance relies on the influence it bears on other properties of graphs such as resilience, or prediction of missing connections. Nevertheless, ...
We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed fro ...
Let c denote the largest constant such that every C-6-free graph G contains a bipartite and C-4-free subgraph having a fraction c of edges of G. Gyori, Kensell and Tompkins showed that 3/8
Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...
The topology of a mobile wireless network changes over time. Maintaining routes between all nodes requires the continuous transmission of control information, which consumes precious power and bandwidth resources. Many routing protocols have been developed ...
The goal of this document is to provide a generalmethod for the computational approach to the topology and geometry of compact Riemann surfaces. The approach is inspired by the paradigms of object oriented programming. Our methods allow us in particular to ...
This thesis is devoted to crossing patterns of edges in topological graphs. We consider the following four problems: A thrackle is a graph drawn in the plane such that every pair of edges meet exactly once: either at a common endpoint or in a proper crossi ...
Let r and w be a fixed positive numbers, w < r. In a bold drawing of a graph, every vertex is represented by a disk of radius r, and every edge by a narrow rectangle of width w. We solve a problem of van Kreveld [K09] by showing that every graph admits a b ...
We provide a tight approximate characterization of the n-dimensional product multicommodity flow (PMF) region for a wireless network of n nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in bo ...
Wireless routing based on an embedding of the connectivity graph is a very promising technique to overcome shortcomings of geographic routing and topology-based routing. This is of particular interest when either absolute coordinates for geographic routing ...
We construct (k±1)-regular graphs which provide sequences of expanders by adding or substracting appropriate 1- factors from given sequences of k- regular graphs. We compute numerical examples in a few cases for which the given sequences are from the work ...
In this paper we propose a set of necessary and sufficient conditions under which the throughput in an ad-hoc network can remain constant as the number of nodes n increases. Throughput refers to the minimum achievable rate between a source-destination pair ...
