Now showing items 1-20 of 20

  • Acyclic edge colourings of graphs with large girth 

    Cai, Xing Shi; Perarnau Llobet, Guillem; Reed, Bruce; Watts, Adam Bene (2016-11-03)
    Article
    Open Access
    An edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every e > 0, there exists a g = g(e) such that if G has maximum degree ¿ and girth at least ...
  • An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs 

    Abiad, Aida; Fiol Mora, Miquel Àngel; Haemers, Willem H.; Perarnau Llobet, Guillem (2014)
    Conference report
    Open Access
    We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by ...
  • Búsqueda de comunidades en grafos grandes mediante configuraciones implícitas de vectores 

    Muntés Mulero, Víctor; Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián (PUBL. UNIVERSIDAD DE ZARAGOZA, 2009)
    Conference report
    Open Access
    Presentamos el algoritmo OCA para buscar comunidades solapadas en grafos grandes, como por ejemplo la Wikipedia con 1,6×107 nodos y 1,8×108 aristas. OCA se basa en la búsqueda iterativa de subconjuntos localmente óptimos ...
  • Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture 

    Chapuy, G.; Perarnau Llobet, Guillem (2018-09-17)
    Article
    Restricted access - publisher's policy
    A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, ...
  • Continuous symmetry and shape measures 

    Perarnau Llobet, Guillem; Pfeifle, Julián; Saludes Closa, Jordi (Centre de Recerca Matemàtica, 2010-06)
    Part of book or chapter of book
    Open Access
  • Counting independent sets in cubic graphs of given girth 

    Perarnau Llobet, Guillem; Perkins, Will (2018-09-26)
    Article
    Restricted access - publisher's policy
    We prove a tight upper bound on the independence polynomial (and total number of independent sets) of cubic graphs of girth at least 5. The bound is achieved by unions of the Heawood graph, the point/line incidence graph ...
  • Critical percolation on random regular graphs 

    Joos, Felix; Perarnau Llobet, Guillem (2018-03-20)
    Article
    Open Access
    We show that for all $ d\in \{3,\ldots ,n-1\}$ the size of the largest component of a random $ d$-regular graph on $ n$ vertices around the percolation threshold $ p=1/(d-1)$ is $ \Theta (n^{2/3})$, with high probability. ...
  • Decomposition of bounded degree graphs into C4-free subgraphs 

    Kang, Ross; Perarnau Llobet, Guillem (2014-10-15)
    Article
    Open Access
    We prove that every graph with maximum degree ∆ admits a partition of its edges into O(√∆) parts (as ∆→∞) none of which contains C4 as a subgraph. This bound is sharp up to a constantfactor. Our proof uses an iterated ...
  • Desenvolupament d'una càmera digital per a la visió estéreo en temps real. 

    Lisa-Mingo, Ferran; Perarnau Llobet, Guillem (2008-12-04)
    Audiovisual
    Open Access
  • Fast recoloring of sparse graphs 

    Bousquet, Nicolas; Perarnau Llobet, Guillem (2015-09-07)
    Article
    Open Access
    In this paper, we show that for every graph of maximum average degree bounded away from d and any two (d + 1)-colorings of it, one can transform one coloring into the other one within a polynomial number of vertex recolorings ...
  • How to determine if a random graph with a fixed degree sequence has a giant component 

    Joos, Felix; Perarnau Llobet, Guillem; Rautenbach, Dieter; Reed, Bruce (2017-01-26)
    Article
    Open Access
    For a fixed degree sequence D=(d1,…,dn) , let G(D) be a uniformly chosen (simple) graph on {1,…,n} where the vertex i has degree di . In this paper we determine whether G(D) has a giant component with high probability, ...
  • Large subgraphs without short cycles 

    Foucaud, Florent; Krivelevich, Michael; Perarnau Llobet, Guillem (2015-01-06)
    Article
    Open Access
    We study two extremal problems about subgraphs excluding a family F of graphs. i) Among all graphs with m edges, what is the smallest size f(m, F) of a largest F–free subgraph? ii) Among all graphs with minimum degree d ...
  • Matchings in random biregular bipartite graphs 

    Perarnau Llobet, Guillem; Petridis, Georgios (2013-03-24)
    Article
    Open Access
    We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random ...
  • On the relation between graph distance and Euclidean distance in random geometric graphs 

    Díaz Cort, Josep; Dieter Wilhelm, Mitsche; Perarnau Llobet, Guillem; Pérez Giménez, Xavier (2016-09-01)
    Article
    Open Access
    Given any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean distance and by dE(u, v) their graph distance. The problem of finding upper bounds on dG(u, v) conditional on dE(u, v) ...
  • 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 the treewidth and related parameters of random geometric graphs 

    Mitsche, Dieter; Perarnau Llobet, Guillem (2017-06-22)
    Article
    Restricted access - publisher's policy
    We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ¿ G(n, r) in [0, v n] 2 . More precisely, let rc denote the threshold radius for the appearance of the giant component in G(n, r). ...
  • Overlapping community search for social networks 

    Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián; Muntés Mulero, Víctor (IEEE Press. Institute of Electrical and Electronics Engineers, 2010)
    Conference report
    Open Access
    Finding decompositions of a graph into a family of clusters is crucial to understanding its underlying structure. While most existing approaches focus on partitioning the nodes, real-world datasets suggest the presence ...
  • Probabilistic methods and coloring problems in graphs 

    Perarnau Llobet, Guillem (Universitat Politècnica de Catalunya, 2010-06)
    Master thesis
    Open Access
    Aquest projecte està dedicat a estudiar el k-èssim nombre cromàtic generalitzat que sorgeix de les descomposicions Low Tree--Depth en grafs usant mètodes probabilístics.. Una extensió natural del nombre cromàtic d'un graf ...
  • Rainbow spanning subgraphs in bounded edge–colourings of graphs with large minimum degree 

    Cano Vila, María del Pilar; Perarnau Llobet, Guillem; Serra Albó, Oriol (2017-08-01)
    Article
    Open Access
    We study the existence of rainbow perfect matching and rainbow Hamiltonian cycles in edge–colored graphs where every color appears a bounded number of times. We derive asymptotically tight bounds on the minimum degree of ...
  • Random combinatorial structures with low dependencies : existence and enumeration 

    Perarnau Llobet, Guillem (Universitat Politècnica de Catalunya, 2013-10-01)
    Doctoral thesis
    Open Access
    En aquesta tesi s'estudien diferents problemes en el camp de la combinatòria i la teoria de grafs, utilitzant el mètode probabilístic. Aquesta tècnica, introduïda per Erdős , ha esdevingut una eina molt potent per tal de ...