Recent Submissions

  • 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
    Restricted access - publisher's policy
    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 ...
  • An analogue of Vosper's theorem for extension fields 

    Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles (2017-11-01)
    Article
    Open Access
    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 ...
  • Forbidden subgraphs in the norm graph 

    Ball, Simeon Michael; Pepe, Valentina (2016-04-06)
    Article
    Open Access
    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
    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) ...
  • Revisiting Kneser’s theorem for field extensions 

    Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles (2017-05-31)
    Article
    Open Access
    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
    Open Access
    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
    Open Access
    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
    Open Access
    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 ...

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