Now showing items 1-20 of 32

    • A rainbow Dirac's theorem 

      Coulson, Matthew John; Perarnau Llobet, Guillem (2020-01-01)
      Article
      Open Access
      A famous theorem of Dirac states that any graph on n vertices with minimum degree at least n/2 has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton ...
    • 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 ...
    • AM2: Examen MQ: primavera 2019 

      Perarnau Llobet, Guillem (Universitat Politècnica de Catalunya, 2019-04-03)
      Exam
      Restricted access to the UPC academic community
    • 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
      Open Access
      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
      Open Access
      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
    • Diameter and stationary distribution of random r-out digraphs 

      Addario-Berry, Louigi; Balle, Borja; Perarnau Llobet, Guillem (2020-08-07)
      Article
      Open Access
      Let D(n, r) be a random r-out regular directed multigraph on the set of vertices {1, . . . , n}. In this work, we establish that for every r = 2, there exists ¿r > 0 such that diam(D(n, r)) = (1 + ¿r + o(1)) logr n. The ...
    • Existence of spanning F-free subgraphs with large minimum degree 

      Perarnau Llobet, Guillem; Reed, Bruce (2016-12-07)
      Article
      Restricted access - publisher's policy
      Let F be a family of graphs and let d be large enough. For every d-regular graph G, we study the existence of a spanning F-free subgraph of G with large minimum degree. This problem is well understood if F does not contain ...
    • 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 ...
    • Frozen (¿ + 1)-colourings of bounded degree graphs 

      Bonamy, Marthe; Bousquet, Nicolas; Perarnau Llobet, Guillem (2020-10-19)
      Article
      Restricted access - publisher's policy
      Let G be a graph on n vertices and with maximum degree ¿, and let k be an integer. The k-recolouring graph of G is the graph whose vertices are k-colourings of G and where two k-colourings are adjacent if they differ at ...
    • 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, ...
    • 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 (Institute of Electrical and Electronics Engineers (IEEE), 2016)
      Conference report
      Open Access
      The traditional Erdos-Renyi model of a random network is of little use in modelling the type of complex networks which modern researchers study. In this graph, every pair of vertices is equally likely to be connected by ...
    • Improved bounds for randomly sampling colorings via linear programming 

      Chen, Sitan; Delcourt, Michelle; Moitra, Ankur; Perarnau Llobet, Guillem; Postle, Luke (2019)
      Conference report
      Restricted access - publisher's policy
      A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of k-colorings of a graph G on n vertices with maximum degree ¿ is rapidly mixing for k = ¿ + 2. In FOCS 1999, Vigoda ...
    • 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 ...
    • Local convergence and stability of tight bridge-addable classes 

      Chapuy, G.; Perarnau Llobet, Guillem (Canadian Mathematical Society, 2020-06-01)
      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. The authors recently proved a conjecture of McDiarmid, ...