Now showing items 1-15 of 15

    • Clique is hard on average for regular resolution 

      Atserias, Albert; Bonacina, Ilario; De Rezende, Susanna F.; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander (Association for Computing Machinery (ACM), 2021-08)
      Article
      Open Access
      We 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 k-clique. This lower bound is optimal up to the multiplicative ...
    • Collective versus hub activation of epidemic phases on networks 

      Ferreira, Silvio C.; Salvador, Renan; Pastor Satorras, Romualdo (AMER PHYSICAL SOC, 2016-03-14)
      Article
      Restricted access - publisher's policy
      We consider a general criterion to discern the nature of the threshold in epidemic models on scale-free (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 

      Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Elsevier, 2021-04-01)
      Article
      Open Access
      Let 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 tower-type for approximating formulas with parity quantifiers 

      Atserias, Albert; Dawar, Anuj (2014-02-01)
      Article
      Open Access
      Kolaitis and Kopparty have shown that for any first-order formula with parity quantifiers over the language of graphs, there is a family of multivariate polynomials of constant-degree that agree with the formula on all but ...
    • Edge crossings in linear arrangements: from theory to algorithms and applications 

      Alemany Puig, Lluís (Universitat Politècnica de Catalunya, 2019-07)
      Master thesis
      Open Access
      Còmput 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 

      Alemany Puig, Lluís; Ferrer Cancho, Ramon (Institute of Physics (IOP), 2020-02-19)
      Article
      Open Access
      In 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 hyper-graphs 

      Larrauri Borroto, Lázaro Alberto (Universitat Politècnica de Catalunya, 2019-07)
      Master thesis
      Restricted access - author's decision
      We 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 

      Rué Perna, Juan José; Mitsche, Dieter (2015-03-20)
      Article
      Open Access
      The 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 

      Perarnau Llobet, Guillem; Serra Albó, Oriol (2010)
      Conference report
      Restricted access - publisher's policy
      The tree-depth 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 zero-one and convergence laws for graphs embeddable on a fixed surface 

      Atserias, Albert; Kreutzer, Stephan; Noy Serrano, Marcos (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
      Conference report
      Open Access
      We show that for no surface except for the plane does monadic second-order logic (MSO) have a zero-one-law - and not even a convergence law - on the class of (connected) graphs embeddable on the surface. In addition we ...
    • Temporal percolation in activity-driven networks 

      Starnini, Michele; Pastor Satorras, Romualdo (2014-03-14)
      Article
      Open Access
      We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity-driven-network model [N. Perra et al., Sci. Rep. 2, 469 ( 2012)]. Building upon an ...
    • The giant component of the directed configuration model revisited 

      Cai, Xing Shi; Perarnau Llobet, Guillem (2021-04-22)
      Article
      Open Access
      We 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 

      Ferrer Cancho, Ramon (Institute of Physics (IOP), 2019-05-09)
      Article
      Open Access
      Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean ...
    • Threshold phenomena in random graphs 

      Redón Orriols, Nil (Universitat Politècnica de Catalunya, 2019-07)
      Bachelor thesis
      Open Access
      In 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 

      Castellano, Claudio; Pastor Satorras, Romualdo (IOP PUBLISHING LTD., 2006-05-03)
      Article
      Restricted access - publisher's policy
      We 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 mean-field theory yields as the main prediction that for ...