Now showing items 21-40 of 54

    • Disecciones de un polígono en el plano proyectivo 

      Noy Serrano, Marcos; Rué Perna, Juan José (Universidad de Valladolid, 2006)
      Conference lecture
      Restricted access - publisher's policy
      En este trabajo obtenemos expresiones explícitas de las funciones generadoras de las triangulaciones y cuadrangulaciones del espacio topológico correspondiente a la supresión de un n-ágono del plano proyectivo real. En el ...
    • Enumeration of chordal planar graphs and maps 

      Castellví Foguet, Jordi; Noy Serrano, Marcos; Requile, Clement (2023-01-01)
      Article
      Open Access
      We determine the number of labelled chordal planar graphs with n vertices, which is asymptotically for a constant and . We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically ...
    • Enumeration of labeled 4-regular planar graphs 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2017-08-01)
      Article
      Open Access
      In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ...
    • 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 ...
    • Enumeration of labelled 4-regular planar graphs II: asymptotics 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2023-05)
      Article
      Open Access
      This work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled ...
    • FONAMENTS DE LA MATEMÀTICA | EXTRAORDINARI 

      Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 2023-06-29)
      Exam
      Restricted access to the UPC academic community
    • FONAMENTS DE LA MATEMÀTICA | FINAL 

      Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 2024-01-18)
      Exam
      Restricted access to the UPC academic community
    • FONAMENTS DE LA MATEMÀTICA | PARCIAL 

      Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 2023-10-30)
      Exam
      Restricted access to the UPC academic community
    • Further results on random cubic planar graphs 

      Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (2020-06)
      Article
      Open Access
      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 ...
    • Geometric tree graphs of points in convex position 

      Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Márquez Pérez, Alberto; Mora Giné, Mercè; Noy Serrano, Marcos (1997)
      Article
      Open Access
      Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are non-crossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent ...
    • Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena 

      Giménez Llach, Omer; Noy Serrano, Marcos; Rué Perna, Juan José (Edicions de la Universitat de Lleida (UdL), 2008)
      Conference lecture
      Restricted access - publisher's policy
      Consider a family T of 3-connected graphs, and let G be the class of graphs whose 3-connected components are graphs in T . We present a general framework for analyzing such graphs classes based on singularity analysis of ...
    • Graphs of non-crossing perfect matchings 

      Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Noy Serrano, Marcos (2001)
      Article
      Open Access
      Let Pn be a set of n = 2m points that are the vertices of a convex polygon, and let Mm be the graph having as vertices all the perfect matchings in the point set Pn whose edges are straight line segments and do not cross, ...
    • Identities for non-crossing graphs and multigraphs 

      Albiol, Rubén; Noy Serrano, Marcos (2008-12)
      Article
      Restricted access - publisher's policy
      We refine an identity between the numbers of certain non-crossing graphs and multigraphs, by modifying a bijection found by P. Podbrdský [A bijective proof of an identity for noncrossing graphs, Discrete Math. 260 (2003) ...
    • Isolated cycles of critical random graphs 

      Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Society for Industrial and Applied Mathematics (SIAM), 2017)
      Conference report
      Open Access
      Consider the Erdos-Renyi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of n2 edges. Let L be a set of positive integers. For any number of edges M 6n/2 + O(n 2/3 ), we compute ...
    • Limiting probabilities of first order properties of random sparse graphs and hypergraphs 

      Larrauri Borroto, Lázaro Alberto; Müller, Tobias; Noy Serrano, Marcos (2021-08-18)
      Article
      Open Access
      Let Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is well-known undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ...
    • On matroids determined by their Tutte polynomials 

      Mier Vinué, Anna de; Noy Serrano, Marcos (2005)
      Article
      Restricted access - publisher's policy
      A matroid is T-unique if it is determined up to isomorphism by its Tutte polynomial. Known T-unique matroids include projective and affine geometries of rank at least four, wheels, whirls, free and binary spikes, and certain ...
    • On the diameter of random planar graphs 

      Chapuy, G.; Fusy, Éric; Giménez Llach, Omer; Noy Serrano, Marcos (2015)
      Article
      Open Access
      We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that {equation presented} for ˜ small ...
    • On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1) 

      Goodall, Andrew; Merino, Criel; Mier Vinué, Anna de; Noy Serrano, Marcos (2010)
      Conference report
      Open Access
      C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t($K_{n+2}$; 1,−1) = t($K_n$;2,−1). In this work we extend this result by giving a large class of graphs with ...
    • On the expected number of perfect matchings in cubic planar graphs 

      Noy Serrano, Marcos; Rué Perna, Juan José; Requile, Clement (2022-01-01)
      Article
      Open Access
      A well-known conjecture by Lovász and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the ...
    • On the maximum number of cycles in outerplanar and series-parallel graph 

      Mier Vinué, Anna de; Noy Serrano, Marcos (2009)
      Article
      Restricted access - publisher's policy
      Let c(n) be the maximum number of cycles in an outerplanar graph with n vertices. We show that lim $c(n)^{1/n}$ exists and equals β = 1.502837 . . ., where β is a constant related to the recurrence $x_n+1$=1+$x^2_n$, ...