Now showing items 1-20 of 26

• #### A solution to the tennis ball problem ﻿

(2005)
Article
Open Access
We present a complete solution to the so-called 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 ﻿

(2011-04)
Article
Open Access
The Baxter number can be written as $B_n = \sum_0^n \Theta_{k,n-k-1}$. These numbers have first appeared in the enumeration of so-called Baxter permutations; $B_n$ is the number of Baxter permutations of size $n$, and ...
• #### CÀLCUL EN UNA VARIABLE | (Examen extraordinari) ﻿

(Universitat Politècnica de Catalunya, 2019-07-01)
Exam
• #### Counting outerplanar maps ﻿

(2017-04-13)
Article
Open Access
A 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 ﻿

(2008-10)
Article
Open Access
For 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 ﻿

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 labeled 4-regular planar graphs ﻿

(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 ...
• #### Further results on random cubic planar graphs ﻿

(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 ...
• #### Geometric tree graphs of points in convex position ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### On matroids determined by their Tutte polynomials ﻿

(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 ﻿

(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) ﻿

(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 maximum number of cycles in outerplanar and series-parallel graph ﻿

(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+$x^2_n$, ...
• #### On the number of labeled graphs of bounded treewidth ﻿

(2018-06-01)
Article
Open Access
Let 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 ﻿

(2015-03-01)
Article
Open Access
Let 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 zero-one and convergence laws for graphs embeddable on a fixed surface ﻿

(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
Conference report
Open Access
We show that for no surface except for the plane does monadic second-order logic (MSO) have a zero-one-law - and not even a convergence law - on the class of (connected) graphs embeddable on the surface. In addition we ...