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.

Recent Submissions

  • New Moore-like bounds and some optimal families of abelian Cayley mixed graphs 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; López Lorenzo, Nacho (2020-06)
    Article
    Open Access
    Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of Abelian groups. Such groups can be ...
  • Spectra and eigenspaces from regular partitions of Cayley (di)graphs of permutation groups 

    Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (Elsevier, 2020-07-15)
    Article
    Restricted access - publisher's policy
    In this paper, we present a method to obtain regular (or equitable) partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of permutation groups on n letters. We prove that every partition of the ...
  • Equivalent characterizations of the spectra of graphs and applications to measures of distance-regularity 

    Fiol Mora, Miquel Àngel; Fàbrega Canudas, José; Diego Gutierrez, Victor (2020-09)
    Article
    Open Access
    The spectrum of a graph usually provides a lot of information about its combinatorial structure. Moreover,from the spectrum, the so-called predistance polynomials can be defined, as a generalization, for any graph, of the ...
  • Bounded queries to arbitrary sets 

    Lozano Bojados, Antoni (1991-09)
    External research report
    Open Access
    We prove that if P superA[k] = P superA[k+1] for some k and an arbitrary set A, then A is reducible to its complement under a relativized nondeterministic conjunctive reduction. This result shows the first known property ...
  • Relativized and positive separations of [delta sub 2 super p] and [fi sub 2 super p] 

    Lozano Bojados, Antoni; Torán Romero, Jacobo (1989)
    External research report
    Open Access
  • Self-reducible sets of small density 

    Lozano Bojados, Antoni; Torán Romero, Jacobo (1989-11)
    External research report
    Open Access
    We study the complexity of sets that are at the same time self-reducible and sparse or m-reducible to sparse sets. We show that sets of this kind are low for the complexity clases [delta sub 2 super p], [fi sub 2 super p], ...
  • Complejidad de problemas sobre representaciones sucintas de grafos 

    Lozano Bojados, Antoni (1988-05)
    External research report
    Open Access
  • An alternate description of a (q + 1; 8)-cage 

    Abreu, Marien; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Labbate, Domenico (2018-12)
    Article
    Open Access
    Let q >= 2 be a prime power. In this note we present an alternate description of the known (q + 1; 8)-cages which has allowed us to construct small (k; g)–graphs for k =q, q-1, and g = 7; 8 in other papers on this same topic.
  • New small regular graphs of girth 5 

    Abajo, E.; Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Bendala García, Manuel Francisco (2017-08)
    Article
    Open Access
    A (k,g)-graph is a k-regular graph with girth g and a (k,g)-cage is a (k,g)-graph with the fewest possible number of vertices. The cage problem consists of constructing (k,g)-graphs of minimum order n(k,g). We focus on ...
  • The p-restricted edge-connectivity of Kneser graphs 

    Balbuena Martínez, Maria Camino Teófila; Marcote Ordax, Francisco Javier (Elsevier, 2019-02-15)
    Article
    Open Access
    Given a connected graph G and an integer 1¿=¿p¿=¿¿|V(G)|/2¿, a p-restricted edge-cut of G is any set of edges S¿¿¿E(G), if any, such that is not connected and each component of has at least p vertices; and the p-restricted ...
  • Improving bounds on the order of regular graphs of girth 5 

    Abajo Casado, Encarnación; Balbuena Martínez, Maria Camino Teófila; Bendala García, Manuel Francisco; Marcote Ordax, Francisco Javier (2019-10-01)
    Article
    Open Access
    A -graph is a -regular graph with girth and a -cage is a -graph with the fewest possible number of vertices . Constructing -cages and determining the order are both very hard problems. For this reason, an intensive line ...
  • About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs 

    Balbuena Martínez, Maria Camino Teófila; Galeana Sánchez, Hortensia; Guevara Aguirre, Nucuy-kak (2019-06)
    Article
    Open Access
    Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 = l = k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial ...

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