The research of the group focuses on interrelated aspects of combinatorics: Graph theory, Random Graphs, Probabilistic method, Geometric group theory and algebraic methods, Enumerative combinatorics, Combinatorial geometry, and Combinatorial number theory. Some recent research achievements are: Proof of the Maximum Distance Separable codes conjecture for prime fields; solution of a conjecture of Green on the removal lemma for systems of equations in finite fields

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Recent Submissions

  • Enumeration of labelled 4-regular planar graphs 

    Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (2019-08-01)
    Open Access
    We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular ...
  • Further results on random cubic planar graphs 

    Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (2020-06)
    Restricted access - publisher's policy
    We provide precise asymptotic estimates for the number of several classes of labeled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed 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 (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 ...
  • Maximal independent sets and maximal matchings in series-parallel and related graph classes 

    Drmota, Michael; Ramos Garrido, Lander; Requilé, Clément; Rué Perna, Juan José (2020-01-10)
    Open Access
    The goal of this paper is to obtain quantitative results on the number and on the size of maximal independent sets and maximal matchings in several block-stable graph classes that satisfy a proper sub-criticality condition. ...
  • Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups 

    Roy, Mallika; Ventura Capell, Enric (2020-04-01)
    Open Access
    The classical result by Dyer–Scott about fixed subgroups of finite order automor-phisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of ...