Browsing by Author "Noy Serrano, Marcos"
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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 policyEn este trabajo obtenemos expresiones explícitas de las funciones generadoras de las triangulaciones y cuadrangulaciones del espacio topológico correspondiente a la supresión de un nágono del plano proyectivo real. En el ... 
Enumeration of chordal planar graphs and maps
Castellví Foguet, Jordi; Noy Serrano, Marcos; Requile, Clement (20230101)
Article
Open AccessWe 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 4regular planar graphs
Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (20170801)
Article
Open AccessIn this extended abstract, we present the first combinatorial scheme for counting labeled 4regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ... 
Enumeration of labelled 4regular planar graphs
Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (20190801)
Article
Open AccessWe present the first combinatorial scheme for counting labelled 4regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4regular ... 
Enumeration of labelled 4regular planar graphs II: asymptotics
Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (202305)
Article
Open AccessThis work is a followup of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4regular 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, 20230629)
Exam
Restricted access to the UPC academic community 
FONAMENTS DE LA MATEMÀTICA  FINAL
Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 20240118)
Exam
Restricted access to the UPC academic community 
FONAMENTS DE LA MATEMÀTICA  PARCIAL
Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 20231030)
Exam
Restricted access to the UPC academic community 
Further results on random cubic planar graphs
Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (202006)
Article
Open AccessWe 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 AccessGiven a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are noncrossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent ... 
Graph classes with given 3connected 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 policyConsider a family T of 3connected graphs, and let G be the class of graphs whose 3connected components are graphs in T . We present a general framework for analyzing such graphs classes based on singularity analysis of ... 
Graphs of noncrossing perfect matchings
Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Noy Serrano, Marcos (2001)
Article
Open AccessLet 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 noncrossing graphs and multigraphs
Albiol, Rubén; Noy Serrano, Marcos (200812)
Article
Restricted access  publisher's policyWe refine an identity between the numbers of certain noncrossing 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 AccessConsider the ErdosRenyi 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 (20210818)
Article
Open AccessLet Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is wellknown 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 policyA matroid is Tunique if it is determined up to isomorphism by its Tutte polynomial. Known Tunique 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 AccessWe 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 AccessC. 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 (20220101)
Article
Open AccessA wellknown 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 seriesparallel graph
Mier Vinué, Anna de; Noy Serrano, Marcos (2009)
Article
Restricted access  publisher's policyLet 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+$x^2_n$, ...