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  • Enumeration of labelled 4-regular planar graphs 

    Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (2019-08-01)
    Article
    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)
    Article
    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 ...

  • 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)
    Article
    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)
    Article
    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 ...