COMBGRAF  Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
Thu, 23 Mar 2017 00:17:10 GMT
20170323T00:17:10Z

The conjugacy problem in extensions of Thompson's group F
http://hdl.handle.net/2117/102759
The conjugacy problem in extensions of Thompson's group F
Burillo Puig, José; Matucci, Francesco; Ventura Capell, Enric
We solve the twisted conjugacy problem on Thompson’s group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut+(F) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak–Fel’shtyn–Gonçalves in [4] showing that F has property R8, and which can be extended to show that Thompson’s group T also has property R8.
The final publication is available at Springer via http://dx.doi.org/10.1007/s1185601614039
Tue, 21 Mar 2017 17:43:46 GMT
http://hdl.handle.net/2117/102759
20170321T17:43:46Z
Burillo Puig, José
Matucci, Francesco
Ventura Capell, Enric
We solve the twisted conjugacy problem on Thompson’s group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut+(F) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak–Fel’shtyn–Gonçalves in [4] showing that F has property R8, and which can be extended to show that Thompson’s group T also has property R8.

Digraphs with walks of equal length between vertices
http://hdl.handle.net/2117/102020
Digraphs with walks of equal length between vertices
Fiol Mora, Miquel Àngel; Alegre, Ignasi; Andrés Yebra, José Luís; Fàbrega Canudas, José
Tue, 07 Mar 2017 09:48:03 GMT
http://hdl.handle.net/2117/102020
20170307T09:48:03Z
Fiol Mora, Miquel Àngel
Alegre, Ignasi
Andrés Yebra, José Luís
Fàbrega Canudas, José

Correlation among runners and some results on the lonely runner conjecture
http://hdl.handle.net/2117/101787
Correlation among runners and some results on the lonely runner conjecture
Perarnau, Guillem; Serra Albó, Oriol
The Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where all of them are far enough from the origin. We study the correlation among the time that runners spend close to the origin. By means of these correlations, we improve a result of Chen on the gap of loneliness. In the last part, we introduce dynamic interval graphs to deal with a weak version of the conjecture thus providing a new result related to the invisible runner theorem of Czerwi´nski and Grytczuk.
Wed, 01 Mar 2017 12:12:35 GMT
http://hdl.handle.net/2117/101787
20170301T12:12:35Z
Perarnau, Guillem
Serra Albó, Oriol
The Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where all of them are far enough from the origin. We study the correlation among the time that runners spend close to the origin. By means of these correlations, we improve a result of Chen on the gap of loneliness. In the last part, we introduce dynamic interval graphs to deal with a weak version of the conjecture thus providing a new result related to the invisible runner theorem of Czerwi´nski and Grytczuk.

Rainbow perfect matchings in rpartite graph structures
http://hdl.handle.net/2117/101772
Rainbow perfect matchings in rpartite graph structures
Cano Vila, María del Pilar; Perarnau, Guillem; Serra Albó, Oriol
A matching M in an edge–colored (hyper)graph is rainbow if each pair of edges in M have distinct colors. We extend the result of Erdos and Spencer on the existence of rainbow perfect matchings in the complete bipartite graph Kn,n to complete bipartite multigraphs, dense regular bipartite graphs and complete rpartite runiform hypergraphs. The proof of the results use the Lopsided version of the Local Lovász Lemma.
Wed, 01 Mar 2017 10:40:23 GMT
http://hdl.handle.net/2117/101772
20170301T10:40:23Z
Cano Vila, María del Pilar
Perarnau, Guillem
Serra Albó, Oriol
A matching M in an edge–colored (hyper)graph is rainbow if each pair of edges in M have distinct colors. We extend the result of Erdos and Spencer on the existence of rainbow perfect matchings in the complete bipartite graph Kn,n to complete bipartite multigraphs, dense regular bipartite graphs and complete rpartite runiform hypergraphs. The proof of the results use the Lopsided version of the Local Lovász Lemma.

A geometric approach to dense Cayley digraphs of finite Abelian groups
http://hdl.handle.net/2117/101763
A geometric approach to dense Cayley digraphs of finite Abelian groups
Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia
We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. A dilating technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree d = 3, contains digraphs with the current best known density.
Wed, 01 Mar 2017 09:28:31 GMT
http://hdl.handle.net/2117/101763
20170301T09:28:31Z
Aguiló Gost, Francisco de Asis L.
Fiol Mora, Miquel Àngel
Pérez Mansilla, Sonia
We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. A dilating technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree d = 3, contains digraphs with the current best known density.

Perspectivas en combinatoria
http://hdl.handle.net/2117/101761
Perspectivas en combinatoria
Noy Serrano, Marcos; Serra Albó, Oriol
Wed, 01 Mar 2017 09:06:19 GMT
http://hdl.handle.net/2117/101761
20170301T09:06:19Z
Noy Serrano, Marcos
Serra Albó, Oriol

Classifing stars: a comparison between clasical, genetic and neural network algorithms
http://hdl.handle.net/2117/100683
Classifing stars: a comparison between clasical, genetic and neural network algorithms
Hernández Pajares, Manuel; Comellas Padró, Francesc de Paula; Monte Moreno, Enrique
Wed, 08 Feb 2017 13:26:04 GMT
http://hdl.handle.net/2117/100683
20170208T13:26:04Z
Hernández Pajares, Manuel
Comellas Padró, Francesc de Paula
Monte Moreno, Enrique

Some spectral and quasispectral characterizations of distanceregular graphs
http://hdl.handle.net/2117/100654
Some spectral and quasispectral characterizations of distanceregular graphs
Abiad, Aida; Van Dam, Edwin R; Fiol Mora, Miquel Àngel
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distanceregular graph. By using the preintersection numbers we give some new spectral and quasispectral characterizations of distanceregularity, in particular for graphs with large girth or large oddgirth. (C) 2016 Published by Elsevier Inc.
© <2016>. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
Wed, 08 Feb 2017 08:23:34 GMT
http://hdl.handle.net/2117/100654
20170208T08:23:34Z
Abiad, Aida
Van Dam, Edwin R
Fiol Mora, Miquel Àngel
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distanceregular graph. By using the preintersection numbers we give some new spectral and quasispectral characterizations of distanceregularity, in particular for graphs with large girth or large oddgirth. (C) 2016 Published by Elsevier Inc.

The spectral excess theorem for distanceregular graphs having distanced graph with fewer distinct eigenvalues
http://hdl.handle.net/2117/100474
The spectral excess theorem for distanceregular graphs having distanced graph with fewer distinct eigenvalues
Fiol Mora, Miquel Àngel
Let Gamma be a distanceregular graph with diameter d and Kneser graph K = Gamma(d), the distanced graph of Gamma. We say that Gamma is partially antipodal when K has fewer distinct eigenvalues than Gamma. In particular, this is the case of antipodal distanceregular graphs (K with only two distinct eigenvalues) and the socalled halfantipodal distanceregular graphs (K with only one negative eigenvalue). We provide a characterization of partially antipodal distanceregular graphs (among regular graphs with d + 1 distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a more general version of the socalled spectral excess theorem, which allows us to characterize those distanceregular graphs which are halfantipodal, antipodal, bipartite, or with Kneser graph being strongly regular.
The final publication is available at Springer via http://dx.doi.org/10.1007/s1080101506546
Thu, 02 Feb 2017 09:38:37 GMT
http://hdl.handle.net/2117/100474
20170202T09:38:37Z
Fiol Mora, Miquel Àngel
Let Gamma be a distanceregular graph with diameter d and Kneser graph K = Gamma(d), the distanced graph of Gamma. We say that Gamma is partially antipodal when K has fewer distinct eigenvalues than Gamma. In particular, this is the case of antipodal distanceregular graphs (K with only two distinct eigenvalues) and the socalled halfantipodal distanceregular graphs (K with only one negative eigenvalue). We provide a characterization of partially antipodal distanceregular graphs (among regular graphs with d + 1 distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a more general version of the socalled spectral excess theorem, which allows us to characterize those distanceregular graphs which are halfantipodal, antipodal, bipartite, or with Kneser graph being strongly regular.

Fast calculation of entropy with Zhang's estimator
http://hdl.handle.net/2117/100157
Fast calculation of entropy with Zhang's estimator
Lozano Bojados, Antoni; Casas Fernández, Bernardino; Bentz, Chris; Ferrer Cancho, Ramon
Entropy is a fundamental property of a repertoire. Here, we present an efficient algorithm to estimate the entropy of types with the help of Zhang’s estimator. The algorithm takes advantage of the fact that the number of different frequencies in a text is in general much smaller than the number of types. We justify the convenience of the algorithm by means of an analysis of the statistical properties of texts from more than 1000 languages. Our work opens up various possibilities for future research.
Fri, 27 Jan 2017 08:06:04 GMT
http://hdl.handle.net/2117/100157
20170127T08:06:04Z
Lozano Bojados, Antoni
Casas Fernández, Bernardino
Bentz, Chris
Ferrer Cancho, Ramon
Entropy is a fundamental property of a repertoire. Here, we present an efficient algorithm to estimate the entropy of types with the help of Zhang’s estimator. The algorithm takes advantage of the fact that the number of different frequencies in a text is in general much smaller than the number of types. We justify the convenience of the algorithm by means of an analysis of the statistical properties of texts from more than 1000 languages. Our work opens up various possibilities for future research.