Browsing by Subject "Random graphs"
Now showing items 115 of 15

Clique is hard on average for regular resolution
(Association for Computing Machinery (ACM), 202108)
Article
Open AccessWe prove that for k ≪ 4√n regular resolution requires length nΩ(k) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a kclique. This lower bound is optimal up to the multiplicative ... 
Collective versus hub activation of epidemic phases on networks
(AMER PHYSICAL SOC, 20160314)
Article
Restricted access  publisher's policyWe consider a general criterion to discern the nature of the threshold in epidemic models on scalefree (SF) networks. Comparing the epidemic lifespan of the nodes with largest degrees with the infection time between them, ... 
Cycles of given lengths in unicyclic components in sparse random graphs
(Elsevier, 20210401)
Article
Open AccessLet L be subset of {3,4,…} and let Xn,M(L) be the number of cycles belonging to unicyclic components whose length is in L in the random graph G(n,M). We find the limiting distribution of Xn,M(L) in the subcritical regime ... 
Degree lower bounds of towertype for approximating formulas with parity quantifiers
(20140201)
Article
Open AccessKolaitis and Kopparty have shown that for any firstorder formula with parity quantifiers over the language of graphs, there is a family of multivariate polynomials of constantdegree that agree with the formula on all but ... 
Edge crossings in linear arrangements: from theory to algorithms and applications
(Universitat Politècnica de Catalunya, 201907)
Master thesis
Open AccessCòmput del nombre de creuaments C en un graf quan els vèrtexos estan distribuïts en arranjaments lineals, del valor exacte de la variància de C en arranjaments lineals uniformement aleatoris. Anàlisi de propietats estadístiques ... 
Edge crossings in random linear arrangements
(Institute of Physics (IOP), 20200219)
Article
Open AccessIn spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1D lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. ... 
First order logic of sparse hypergraphs
(Universitat Politècnica de Catalunya, 201907)
Master thesis
Restricted access  author's decisionWe give a generalization the results from Lynch on the convergence law for sparse random graphs to sparse random hypergraphs. 
On the limiting distribution of the metric dimension for random forests
(20150320)
Article
Open AccessThe metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric ... 
On the tree depth of random graphs
(2010)
Conference report
Restricted access  publisher's policyThe treedepth of a graph G is a parameter that plays a crucial role in the theory of bounded expansion classes and has been introduced under numerous names. We describe the asymptotic behaviour of this parameter in the ... 
On zeroone and convergence laws for graphs embeddable on a fixed surface
(Schloss Dagstuhl  LeibnizZentrum für Informatik, 2018)
Conference report
Open AccessWe show that for no surface except for the plane does monadic secondorder logic (MSO) have a zeroonelaw  and not even a convergence law  on the class of (connected) graphs embeddable on the surface. In addition we ... 
Temporal percolation in activitydriven networks
(20140314)
Article
Open AccessWe study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activitydrivennetwork model [N. Perra et al., Sci. Rep. 2, 469 ( 2012)]. Building upon an ... 
The giant component of the directed configuration model revisited
(20210422)
Article
Open AccessWe prove a law of large numbers for the order and size of the largest strongly connected component in the directed configuration model. Our result extends previous work by Cooper and Frieze (2004). 
The sum of edge lengths in random linear arrangements
(Institute of Physics (IOP), 20190509)
Article
Open AccessSpatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is twodimensional and until recently and traditionally, the metric that was usually considered was the Euclidean ... 
Threshold phenomena in random graphs
(Universitat Politècnica de Catalunya, 201907)
Bachelor thesis
Open AccessIn the 1950s, random graphs appeared for the first time in a result of the prolific hungarian mathematician Pál Erd\H{o}s. Since then, interest in random graph theory has only grown up until now. In its first stages, the ... 
Zero temperature Glauber dynamics on complex networks
(IOP PUBLISHING LTD., 20060503)
Article
Restricted access  publisher's policyWe study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of meanfield theory yields as the main prediction that for ...