The research of COMBGRAPH deals with extremal problems in Combinatorics and Graph Theory. The study of discrete configurations (which optimize one or several parameters) is a main source of challenges. This project includes problems related to: the optimization of metric parameters of graphs, coloring and labeling problems, connectivity and reliability, configurations in graphs, symmetric structures, tilings, algorithm design, and signal processing techniques. All these problems are mainly motivated by applications in network design, analysis for communication protocols, multiprocessor systems, and complex networks. We use combinatorial and algebraic techniques in graph theory, Fourier analysis and polynomial and probabilistic methods in combinatorics, together with techniques close to the combinatorial nature of the problems under consideration. This project gathers the activity of a well-established research group with almost 30 years of experience and with international projection.

http://futur.upc.edu/COMBGRAF

Enviaments recents

  • An analogue of Vosper's theorem for extension fields 

    Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles (2017-11-01)
    Article
    Accés obert
    We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result ...
  • Combinatorics in the Art of the Twentieth Century 

    Barrière Figueroa, Eulalia (2017)
    Text en actes de congrés
    Accés obert
    This paper is motivated by a question I asked myself: How can combinatorial structures be used in a work of art? Immediately, other questions arose: Whether there are artists that work or think combinatorially? If so, what ...
  • Forbidden subgraphs in the norm graph 

    Ball, Simeon Michael; Pepe, Valentina (2016-04-06)
    Article
    Accés obert
    We show that the norm graph with n vertices about View the MathML source edges, which contains no copy of the complete bipartite graph Kt,(t-1)!+1, does not contain a copy of Kt+1,(t-1)!-1.
  • 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
    Accés obert
    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) ...
  • Revisiting Kneser’s theorem for field extensions 

    Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles (2017-05-31)
    Article
    Accés restringit per política de l'editorial
    A Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all ...
  • Transformation and decomposition of clutters into matroids 

    Martí Farré, Jaume; Mier Vinué, Anna de (2017-05-25)
    Article
    Accés restringit per política de l'editorial
    A clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of ...
  • Random subgraphs make identification affordable 

    Foucaud, Florent; Perarnau, Guillem; Serra Albó, Oriol (2017-01-02)
    Article
    Accés obert
    An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the ...
  • On star forest ascending subgraph decomposition 

    Aroca Farrerons, José María; Lladó Sánchez, Ana M. (2017-02-03)
    Article
    Accés obert
    The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with (n+12) edges admits an edge decomposition G=H1¿¿¿Hn such that Hi has i edges and it is isomorphic to a subgraph of Hi+1, i=1,…,n-1. We ...
  • Approximate results for rainbow labelings 

    Lladó Sánchez, Ana M.; Miller, Mirka (2017-03)
    Article
    Accés obert
    A simple graph G=(V,E) is said to be antimagic if there exists a bijection f:E¿[1,|E|] such that the sum of the values of f on edges incident to a vertex takes different values on distinct vertices. The graph G is distance ...
  • Proinsulin protects against age-related cognitive loss through anti-inflammatory convergent pathways 

    Corpas, Ruben; Hernández Pinto, Alberto M.; Porquet, David; Hernández Sánchez, Catalina; Bosch, Fatima; Ortega Aznar, Arantxa; Comellas Padró, Francesc de Paula; de la Rosa, Enrique J.; Sanfeliu Pujol, Coral (2017-09-01)
    Article
    Accés restringit per política de l'editorial
    Brain inflammaging is increasingly considered as contributing to age-related cognitive loss and neurodegeneration. Despite intensive research in multiple models, no clinically effective pharmacological treatment has been ...
  • (Di)graph products, labelings and related results 

    López Masip, Susana Clara (2017-07)
    Article
    Accés restringit per política de l'editorial
    Gallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can ...
  • On subsets of the normal rational curve 

    Ball, Simeon Michael; De Beule, Jan (2017-06-01)
    Article
    Accés restringit per política de l'editorial
    A normal rational curve of the (k-1) -dimensional projective space over Fq is an arc of size q+1 , since any k points of the curve span the whole space. In this paper, we will prove that if q is odd, then a subset of size ...

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