Compute-and-forward (CF) is a technique which exploits broadcast and superposition in wireless networks. In this paper, the CF energy benefit is studied for networks with unicast sessions and modeled by connected graphs. This benefit is defined as the rati ...
We study the extinction time tau of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degr ...
A Kneser graph KG(n,k) is a graph whose vertices are in oneto-one correspondence with k -element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect. A famous result due to Lowisz states that the chromatic num ...
This thesis is devoted to the understanding of topological graphs. We consider the following four problems: 1. A \emph{simple topological graph} is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any t ...
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 ...
We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...
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 ...
