Random planar maps and graphs with minimum degree two and three

We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to the core of a random planar graph is of order c log(n) for an explicit constant c. These results provide new information on the structure of random planar graphs.Comment: 32 page

Too much duplicating patterns represent nonregular languages

A constrained term pattern s:phi represents the language of all instances of the term s satisfying the constraint phi. For each variable in s, this constraint specifies the language of its allowed substitutions. The goal of this project is to find efficient and computable properties ensuring non-regularity of the language represented by a set of constrained patterns.. A constrained term pattern s:phi represents the language of all instances of the term s satisfying the constraint phi. For each variable in s, this constraint specifies the language of its allowed substitutions.The goal of this project is to find efficient and computable properties ensuring non-regularity of the language represented by a set of constrained patterns

Maximal Independent Sets and Maximal Matchings in Series-Parallel and Related Graph Classes

We provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in series-parallel graphs (and related graph classes) with n vertices. In particular, our results extend previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988]. We also show that these two parameters converge to a central limit law

The HOM problem is EXPTIME-complete

We define a new class of tree automata with constraints and prove decidability of the emptiness problem for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree languages under tree homomorphisms, like set inclusion, regularity (HOM problem), and finiteness of set difference. Our result also has implications in term rewriting, since the set of reducible terms of a term rewrite system can be described as the image of a tree homomorphism. In particular, we prove that inclusion of sets of normal forms of term rewrite systems can be decided in exponential time. Analogous consequences arise in the context of XML typechecking, since types are defined by tree automata and some type transformations are homomorphic.Peer ReviewedPostprint (published version

Visualización 3D de imágenes biomédicas en formato .OBJ

Este proyecto se basa en la realización de una herramienta de visualización 3D utilizando C como lenguaje de programación y las librerías openGL e ImageMagick. El proyecto permitirá, tras leer el fichero .obj, situar vértices en puntos específicos de un escenario 3D. La unión de estos puntos en bloques de 3 representará un triángulo; en bloques de cuatro, un cuadrado. La agrupación de múltiples polígonos traerá como consecuencia la representación de la silueta de la imagen deseada en 3D, a la que posteriormente se le insertarán las texturas. La representación conjunta de la silueta creada por los polígonos y las texturas pegadas en ella, tendrán como resultado la imagen 3D a color.3Dko bistaratze-erraminta bat egitea da proiektu honen helburua. Horretarako, openGL eta ImageMagick liburutegiak eta C programazio lengoaia erabiliko dira. .obj fitxategia irakurri ondoren, proiektua 3Dko agertoki bateko puntu zehatzetan kokatzea baimentzen du. Puntu hauek hiru blokeetan lotzen dituenean, hirukiak sortzen dira. Lau blokeetan lotzen baldin baditu, aldiz, karratuak. Askotariko poligonoak batzean baldin badira, gura den irudiaren 3Dko silueta irudikatzea lortu ahal izango da. Geroago, silueta horiei ehundurak sartuko zaizkie. Poligonoek eta testurek elkarrekin sortzen duten azken irudia, koloreetan egongo den 3D ko irudia izango dute emaitza bezala.This project is based on the realization of a 3D visualization tool using C as a programming language and openGL and ImageMagick libraries. The project, after reading the .obj file, allows you to place vertices in specific points of a 3D scene. The union of these points into blocks of 3 will represent a triangle; in blocks of four, a square. The grouping of multiple polygons will bring as a consequence the representation of the silhouette of the desired image in 3D, to which later the textures will be insertedThe joint representation of the silhouette created by the polygons and the textures stuck on it, will result in the 3D color image

Visualización 3D de imágenes biomédicas en formato .OBJ

Este proyecto se basa en la realización de una herramienta de visualización 3D utilizando C como lenguaje de programación y las librerías openGL e ImageMagick. El proyecto permitirá, tras leer el fichero .obj, situar vértices en puntos específicos de un escenario 3D. La unión de estos puntos en bloques de 3 representará un triángulo; en bloques de cuatro, un cuadrado. La agrupación de múltiples polígonos traerá como consecuencia la representación de la silueta de la imagen deseada en 3D, a la que posteriormente se le insertarán las texturas. La representación conjunta de la silueta creada por los polígonos y las texturas pegadas en ella, tendrán como resultado la imagen 3D a color.3Dko bistaratze-erraminta bat egitea da proiektu honen helburua. Horretarako, openGL eta ImageMagick liburutegiak eta C programazio lengoaia erabiliko dira. .obj fitxategia irakurri ondoren, proiektua 3Dko agertoki bateko puntu zehatzetan kokatzea baimentzen du. Puntu hauek hiru blokeetan lotzen dituenean, hirukiak sortzen dira. Lau blokeetan lotzen baldin baditu, aldiz, karratuak. Askotariko poligonoak batzean baldin badira, gura den irudiaren 3Dko silueta irudikatzea lortu ahal izango da. Geroago, silueta horiei ehundurak sartuko zaizkie. Poligonoek eta testurek elkarrekin sortzen duten azken irudia, koloreetan egongo den 3D ko irudia izango dute emaitza bezala.This project is based on the realization of a 3D visualization tool using C as a programming language and openGL and ImageMagick libraries. The project, after reading the .obj file, allows you to place vertices in specific points of a 3D scene. The union of these points into blocks of 3 will represent a triangle; in blocks of four, a square. The grouping of multiple polygons will bring as a consequence the representation of the silhouette of the desired image in 3D, to which later the textures will be insertedThe joint representation of the silhouette created by the polygons and the textures stuck on it, will result in the 3D color image

Subgraph statistics in subcritical graph classes

Let H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations [Drmota, Gittenberger, and Morgenbesser, Submitted]. As a case study, we obtain explicit expressions for the number of triangles and cycles of length 4 in the family of series-parallel graphs.Postprint (author's final draft

Too much duplicating patterns represent nonregular languages

A constrained term pattern s:phi represents the language of all instances of the term s satisfying the constraint phi. For each variable in s, this constraint specifies the language of its allowed substitutions. The goal of this project is to find efficient and computable properties ensuring non-regularity of the language represented by a set of constrained patterns.. A constrained term pattern s:phi represents the language of all instances of the term s satisfying the constraint phi. For each variable in s, this constraint specifies the language of its allowed substitutions.The goal of this project is to find efficient and computable properties ensuring non-regularity of the language represented by a set of constrained patterns

Maximal independent sets and maximal matchings in series-parallel and related graph classes

We provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in seriesparallel graphs (and related graph classes) with n vertices. In particular, our results extend previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988]. We also show that these two parameters converge to a central limit law.Postprint (author's final draft