Browsing by Author "Noy Serrano, Marcos"

A solution to the tennis ball problem
Mier Vinué, Anna de; Noy Serrano, Marcos (2005)
Article
Open AccessWe present a complete solution to the socalled tennis ball problem, which is equivalent to counting the number of lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution ... 
Bijections for Baxter families and related objects
Felsner, Stefan; Fusy, Éric; Noy Serrano, Marcos; Orden, David (201104)
Article
Open AccessThe Baxter number can be written as $B_n = \sum_0^n \Theta_{k,nk1}$. These numbers have first appeared in the enumeration of socalled Baxter permutations; $B_n$ is the number of Baxter permutations of size $n$, and ... 
Counting outerplanar maps
Geffner, I.; Noy Serrano, Marcos (20170413)
Article
Open AccessA map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice ... 
Counting polygon dissections in the projective plane
Noy Serrano, Marcos; Rué Perna, Juan José (200810)
Article
Open AccessFor each value of k ≥ 2, we determine the number pn of ways of dissecting a polygon in the projective plane into n subpolygons with k + 1 sides each. In particular, if k = 2 we recover a result of Edelman and Reiner (1997) ... 
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 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 ... 
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 ... 
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 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+$x^2_n$, ... 
On the number of labeled graphs of bounded treewidth
Baste, Julien; Noy Serrano, Marcos; Sau, Ignasi (20180601)
Article
Restricted access  publisher's policyLet be Tnk the number of labeled graphs on vertices and treewidth at most (equivalently, the number o<f labeled partial trees). We show that [...] for k>1 and some explicit absolute constant c>0. Disregarding terms depending ... 
On the probability of planarity of a random graph near the critical point
Noy Serrano, Marcos; Ravelomanana, Vlady; Rue, Juanjo (20150301)
Article
Open AccessLet G(n, M) be the uniform random graph with n vertices and M edges. Erdos and Renyi (1960) conjectured that the limiting probability; lim(n >infinity) Pr{G(n, n/2) is planar}; exists and is a constant strictly between 0 ... 
On zeroone and convergence laws for graphs embeddable on a fixed surface
Atserias, Albert; Kreutzer, Stephan; Noy Serrano, Marcos (Schloss Dagstuhl  LeibnizZentrum für Informatik, 2018)
Conference report
Open AccessWe show that for no surface except for the plane does monadic secondorder logic (MSO) have a zeroonelaw  and not even a convergence law  on the class of (connected) graphs embeddable on the surface. In addition we ... 
Perspectivas en combinatoria
Noy Serrano, Marcos; Serra Albó, Oriol (Real Sociedad Matemática Española, 20161003)
Article
Open Access 
Random cubic planar graphs revisited
Rué Perna, Juan José; Noy Serrano, Marcos; Requile, Clement (Elsevier, 2016)
Other
Restricted access  publisher's policyThe goal of our work is to analyze random cubic planar graphs according to the uniform distribution. More precisely, let G be the class of labelled cubic planar graphs and let gn be the number of graphs with n vertices. ...