Now showing items 1-20 of 30

• #### Activities and coefficients of the Tutte polynomial ﻿

(Universitat Politècnica de Catalunya, 2019-01)
Master thesis
Open Access
Matroids are combinatorial objects that capture abstractly the essence of dependence. The Tutte polynomial, defined for matroids and graphs, has a numerous amount of information about these structures. In this thesis, we ...
• #### A fast and efficient algorithm to identify clusters in networks ﻿

(2008-08-02)
Article
Open Access
A characteristic feature of many relevant real life networks, like the WWW, Internet, transportation and communication networks, or even biological and social networks, is their clustering structure. We discuss in this ...
• #### An eigenvalue characterization of antipodal distance-regular graphs ﻿

(1997-11)
Article
Open Access
Let $\Gamma$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $\Gamma$ is an $r$-antipodal distance-regular graph if and only if the distance graph $\Gamma_d$ ...
• #### Bounded expansion in models of webgraphs ﻿

(2007-10-02)
Article
Open Access
We study the bounded expansion of several models of web graphs. We show that various deterministic graph models for large complex networks have constant bounded expansion.We study two random models of webgraphs, showing ...
• #### Bumblebees: a multiagent combinatorial optimization algorithm inspired by social insect behaviour ﻿

(2009-01-20)
Conference lecture
Open Access
This paper introduces a multiagent optimization algorithm inspired by the collective behavior of social insects. In our method, each agent encodes a possible solution of the problem to solve, and evolves in a way similar ...
• #### Characterizing (l,m)-walk-regularity ﻿

(2009-05)
Article
Open Access
A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ ...
• #### Combinatorial vs. algebraic characterizations of pseudo-distance-regularity around a set ﻿

(2009-06)
External research report
Open Access
Given a simple connected graph $\Gamma$ and a subset of its vertices $C$, the pseudo-distance-regularity around $C$ generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to now, most ...
• #### Construcció de codis correctors a partir de configuracions i grafs ﻿

(Universitat Politècnica de Barcelona. Centre de Càlcul, 1986-06)
Article
Open Access
Se trata de presentar algunas de las relaciones de carácter básicamente combinatorio que es posible encontrar entre dos tipos importantes de estructuras de incidencia, como son los grafos simétricos y las t-configuraciones, ...
• #### Decomposition spaces, incidence algebras and Möbius inversion ﻿

(2014-04-11)
External research report
Open Access
• #### Decomposition spaces, incidence algebras and Möbius inversion I: basic theory ﻿

(2015-12)
External research report
Open Access
This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality ...
• #### Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness ﻿

(2015-12)
External research report
Open Access
This is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space ...
• #### Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals ﻿

(2015-12)
External research report
Open Access
Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra ...
• #### Decomposition spaces in combinatorics ﻿

(2016-12)
External research report
Open Access
A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new ...
• #### Enumeration and random generation of planar maps ﻿

(Universitat Politècnica de Catalunya, 2014-07)
Master thesis
Open Access
This works gives some results on outerplanar maps, which includes a codification of simple outerplanar maps with 3n bits, where n is the number of nodes. It also includes an algorithm to produce random generated maps with ...
• #### Euler: Idees seminals en combinatòria ﻿

(2007-06-20)
Audiovisual
Open Access
De la quantitat ingent de treballs d'Euler, només una part molt minsa està dedicada a la combinatòria. Tanmateix, els pocs problemes combinatoris que Euler tractà han estat punt d'arrencada de desenvolupaments posteriors ...
• #### Genealogía de permutaciones simples de orden una potencia de dos ﻿

(2006-02)
Article
Open Access
The aim of this paper is to show some properties of simple permutations with order a power of two and to give a combinatorial formula to determine its genealogy involving two new operations: the \textit{pasting} operation ...
• #### Matricial realizations of the solutions of the Carlson problem ﻿

(2001)
Article
Open Access
The Klein theorem asserts the existence of a solution of the Carlson problem when a related Littelewood-Richardson sequence exists. Here we present an explicit construction of these matricial solutions.
• #### Modeling complex networks with self-similar outerplanar unclustered graphs ﻿

(2009-01-21)
Article
Open Access
This paper introduces a family of modular, self-similar, small-world graphs with clustering zero. Relevant properties of this family are comparable to those of some networks associated with technological systems with a low ...
• #### On monochromatic solutions of equations in groups ﻿

(2006-01-12)
Article
Open Access
Resum no disponible
• #### Planar unclustered graphs to model technological and biological networks ﻿

(2009-02-25)
Article
Open Access
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in ...