Browsing by Author "Perarnau Llobet, Guillem"
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A rainbow Dirac's theorem
Coulson, Matthew John; Perarnau Llobet, Guillem (20200101)
Article
Open AccessA 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 (20161103)
Article
Open AccessAn 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, 20190403)
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 AccessWe 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 AccessPresentamos 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 bridgeaddable graph classes: the McDiarmidStegerWelsh conjecture
Chapuy, G.; Perarnau Llobet, Guillem (20180917)
Article
Open AccessA class of graphs is bridgeaddable 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, 201006)
Part of book or chapter of book
Open Access 
Correlation among runners and some results on the lonely runner conjecture
Perarnau Llobet, Guillem; Serra Albó, Oriol (20161003)
Article
Open AccessThe Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where ... 
Counting independent sets in cubic graphs of given girth
Perarnau Llobet, Guillem; Perkins, Will (20180926)
Article
Open AccessWe 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 (20180320)
Article
Open AccessWe show that for all $ d\in \{3,\ldots ,n1\}$ the size of the largest component of a random $ d$regular graph on $ n$ vertices around the percolation threshold $ p=1/(d1)$ is $ \Theta (n^{2/3})$, with high probability. ... 
Decomposition of bounded degree graphs into C4free subgraphs
Kang, Ross; Perarnau Llobet, Guillem (20141015)
Article
Open AccessWe 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.
LisaMingo, Ferran; Perarnau Llobet, Guillem (20081204)
Audiovisual
Open Access 
Diameter and stationary distribution of random rout digraphs
AddarioBerry, Louigi; Balle, Borja; Perarnau Llobet, Guillem (20200807)
Article
Open AccessLet D(n, r) be a random rout 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 Ffree subgraphs with large minimum degree
Perarnau Llobet, Guillem; Reed, Bruce (20161207)
Article
Restricted access  publisher's policyLet F be a family of graphs and let d be large enough. For every dregular graph G, we study the existence of a spanning Ffree 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 (20150907)
Article
Open AccessIn 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 (20201019)
Article
Restricted access  publisher's policyLet G be a graph on n vertices and with maximum degree ¿, and let k be an integer. The krecolouring graph of G is the graph whose vertices are kcolourings of G and where two kcolourings 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 (Institute of Electrical and Electronics Engineers (IEEE), 2016)
Conference report
Open AccessThe traditional ErdosRenyi 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 ... 
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 (20170126)
Article
Open AccessFor 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, ... 
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 policyA wellknown conjecture in computer science and statistical physics is that Glauber dynamics on the set of kcolorings 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 (20150106)
Article
Open AccessWe 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 ...