http://sedici.unlp.edu.ar:80/handle/10915/94592 Thu, 29 Oct 2026 11:11:26 GMT 2026-10-29T11:11:26Z http://sedici.unlp.edu.ar:80/handle/10915/190022 Articulo Journal of Noncommutative Geometry; vol. 16, no. 3 We address the study of multiparameter quantum groups (MpQGs) at roots of unity, namely quantum universal enveloping algebras Uq (g) depending on a matrix of parameters q D q=(qᵢⱼ)ᵢ,ⱼ∈I . This is performed via the construction of quantum root vectors and suitable "integral forms” of Uq (g), a restricted one—generated by quantum divided powers and quantum binomial coefficients—and an unrestricted one—where quantum root vectors are suitably renormalized. The specializations at roots of unity of either form are the "MpQGs at roots of unity” we look for. In particular, we study special subalgebras and quotients of our MpQGs at roots of unity—namely, the multiparameter version of small quantum groups—and suitable associated quantum Frobenius morphisms, that link the MpQGs at roots of 1 with MpQGs at 1, the latter being classical Hopf algebras bearing a well precise Poisson-geometrical content. A key point in the discussion, often at the core of our strategy, is that every MpQG is actually a 2-cocycle deformation of the algebra structure of (a lift of) the "canonical” one-parameter quantum group by Jimbo–Lusztig, so that we can often rely on already established results available for the latter. On the other hand, depending on the chosen multiparameter q, our quantum groups yield (through the choice of integral forms and their specializations) different semiclassical structures, namely different Lie coalgebra structures and Poisson structures on the Lie algebra and algebraic group underlying the canonical one-parameter quantum group. Sat, 01 Jan 2022 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/190022 2022-01-01T00:00:00Z We address the study of multiparameter quantum groups (MpQGs) at roots of unity, namely quantum universal enveloping algebras Uq (g) depending on a matrix of parameters q D q=(qᵢⱼ)ᵢ,ⱼ∈I . This is performed via the construction of quantum root vectors and suitable "integral forms” of Uq (g), a restricted one—generated by quantum divided powers and quantum binomial coefficients—and an unrestricted one—where quantum root vectors are suitably renormalized. The specializations at roots of unity of either form are the "MpQGs at roots of unity” we look for. In particular, we study special subalgebras and quotients of our MpQGs at roots of unity—namely, the multiparameter version of small quantum groups—and suitable associated quantum Frobenius morphisms, that link the MpQGs at roots of 1 with MpQGs at 1, the latter being classical Hopf algebras bearing a well precise Poisson-geometrical content. A key point in the discussion, often at the core of our strategy, is that every MpQG is actually a 2-cocycle deformation of the algebra structure of (a lift of) the "canonical” one-parameter quantum group by Jimbo–Lusztig, so that we can often rely on already established results available for the latter. On the other hand, depending on the chosen multiparameter q, our quantum groups yield (through the choice of integral forms and their specializations) different semiclassical structures, namely different Lie coalgebra structures and Poisson structures on the Lie algebra and algebraic group underlying the canonical one-parameter quantum group. http://sedici.unlp.edu.ar:80/handle/10915/164546 Objeto de conferencia XV Congreso Dr. Antonio Monteiro (Bahía Blanca, 5 al 7 de junio de 2019) En 2008 H.P. Sankappanavar introdujo y estudió a las álgebras de semi Heyting como una generalización de las álgebras de Heyting [3]. Más tarde, en 2011, definió a las álgebras de semi Heyting dualmente hemimórficas como una expansión de las álgebras de semi Heyting en términos de un hemimorfismo dual que generaliza la operación de De Morgan y el pseudocomplemento dual [4]. Las álgebras de Nelson fueron definidas por H. Rasiowa en [2]. Existe una relación cercana entre la variedad de las álgebras de Nelson y la variedad de las álgebras de Heyting, la cual fue estudiada por D. Vakarelov [6] y A. Sendlewski [5], entre otros. En [1] se extendió esta construcción en el contexto de las álgebras de semi Heyting y se obtuvo una nueva variedad cuyos miembros se denominaron álgebras de semi Nelson. En esta charla contaremos cómo se puede extender la relación entre las álgebras de semi Heyting y las álgebras de semi Nelson en el marco de las álgebras de semi Heyting dualmente hemimórficas. Para tal fin introduciremos y estudiaremos la variedad de las álgebras de semi Nelson dualmente hemimórficas. En particular, probaremos que la categoría de las álgebras de semi Heyting dualmente hemimórficas es equivalente a la categoría de las álgebras de semi Nelson centradas dualmente hemimórficas. Finalmente estudiaremos el reticulado de congruencias de las álgebras de semi Nelson dualmente hemimórficas. Tue, 01 Jan 2019 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/164546 2019-01-01T00:00:00Z En 2008 H.P. Sankappanavar introdujo y estudió a las álgebras de semi Heyting como una generalización de las álgebras de Heyting [3]. Más tarde, en 2011, definió a las álgebras de semi Heyting dualmente hemimórficas como una expansión de las álgebras de semi Heyting en términos de un hemimorfismo dual que generaliza la operación de De Morgan y el pseudocomplemento dual [4]. Las álgebras de Nelson fueron definidas por H. Rasiowa en [2]. Existe una relación cercana entre la variedad de las álgebras de Nelson y la variedad de las álgebras de Heyting, la cual fue estudiada por D. Vakarelov [6] y A. Sendlewski [5], entre otros. En [1] se extendió esta construcción en el contexto de las álgebras de semi Heyting y se obtuvo una nueva variedad cuyos miembros se denominaron álgebras de semi Nelson. En esta charla contaremos cómo se puede extender la relación entre las álgebras de semi Heyting y las álgebras de semi Nelson en el marco de las álgebras de semi Heyting dualmente hemimórficas. Para tal fin introduciremos y estudiaremos la variedad de las álgebras de semi Nelson dualmente hemimórficas. En particular, probaremos que la categoría de las álgebras de semi Heyting dualmente hemimórficas es equivalente a la categoría de las álgebras de semi Nelson centradas dualmente hemimórficas. Finalmente estudiaremos el reticulado de congruencias de las álgebras de semi Nelson dualmente hemimórficas. http://sedici.unlp.edu.ar:80/handle/10915/164542 Objeto de conferencia XV Congreso Dr. Antonio Monteiro (Bahía Blanca, 5 al 7 de junio de 2019) En [2] los autores generalizan la construcción dada por Vakarelov en [5], donde se establece una relación entre las álgebras de Heyting y las álgebras de Nelson, en el contexto de las álgebras de semi-Heyting [4]. Para lograr este propósito introducen y estudian la variedad de álgebras de semi-Nelson. En esta charla mostraremos que existe una equivalencia entre la categoría de álgebras de semi-Heyting y la categoría de álgebras de semi-Nelson centradas considerando dos construcciones posibles [1]. También presentaremos ciertas conexiones entre la categoría de álgebras de semi-Nelson centradas y algunos resultados obtenidos en [3]. Tue, 01 Jan 2019 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/164542 2019-01-01T00:00:00Z En [2] los autores generalizan la construcción dada por Vakarelov en [5], donde se establece una relación entre las álgebras de Heyting y las álgebras de Nelson, en el contexto de las álgebras de semi-Heyting [4]. Para lograr este propósito introducen y estudian la variedad de álgebras de semi-Nelson. En esta charla mostraremos que existe una equivalencia entre la categoría de álgebras de semi-Heyting y la categoría de álgebras de semi-Nelson centradas considerando dos construcciones posibles [1]. También presentaremos ciertas conexiones entre la categoría de álgebras de semi-Nelson centradas y algunos resultados obtenidos en [3]. http://sedici.unlp.edu.ar:80/handle/10915/164538 Objeto de conferencia The lattice of subvarieties of the variety MG XV Congreso Dr. Antonio Monteiro (Bahía Blanca, 5 al 7 de junio de 2019) Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía.; BL-algebras were introduced by Hájek (see [5]) to formalize fuzzy logics in which the conjunction is interpreted by continuous t-norms over the real interval [0;1]. These algebras form a variety, usually called BL. In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0;1]MV and the Gödel hoop [0;1]G, that is, generated by A = [0;1]MV ⊕ [0;1]G. Though it is well-known that [0;1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0;1]MV are usually called regular elements of A: The main advantage of this approach, is that unlike the work done in [3] and [1], when the number n of generators of the free algebra increase the generating chain remains fixed. This provides a clear insight of the role of the two main blocks of the generating chain in the description of the functions in the free algebra: the role of the regular elements and the role of the dense elements. We have a functional representation for the free algebra FreeMG (n). To define this functions we need to decompose the domain Aⁿ = ([0;1]MV ⊕ [0;1]G)ⁿ in a finite number of pieces. In each piece a function F ∈ FreeMG (n) coincides either with McNaughton functions or functions of FreeG (n). Using [2] and [4] we give a description of the elements in the lattice of subvarieties of the variety MG and the equational characterization of them. Tue, 01 Jan 2019 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/164538 2019-01-01T00:00:00Z Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía. BL-algebras were introduced by Hájek (see [5]) to formalize fuzzy logics in which the conjunction is interpreted by continuous t-norms over the real interval [0;1]. These algebras form a variety, usually called BL. In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0;1]MV and the Gödel hoop [0;1]G, that is, generated by A = [0;1]MV ⊕ [0;1]G. Though it is well-known that [0;1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0;1]MV are usually called regular elements of A: The main advantage of this approach, is that unlike the work done in [3] and [1], when the number n of generators of the free algebra increase the generating chain remains fixed. This provides a clear insight of the role of the two main blocks of the generating chain in the description of the functions in the free algebra: the role of the regular elements and the role of the dense elements. We have a functional representation for the free algebra FreeMG (n). To define this functions we need to decompose the domain Aⁿ = ([0;1]MV ⊕ [0;1]G)ⁿ in a finite number of pieces. In each piece a function F ∈ FreeMG (n) coincides either with McNaughton functions or functions of FreeG (n). Using [2] and [4] we give a description of the elements in the lattice of subvarieties of the variety MG and the equational characterization of them. http://sedici.unlp.edu.ar:80/handle/10915/164533 Publicacion seriada Notas de Lógica Matemática; no. 42 Con el propósito de dar una base para el estudio de temas en el área de Álgebra de la Lógica, fue propuesto y dictado por Marta Sagastume el curso "Álgebra del Cálculo Proposicional" en la Facultad de Ciencias Exactas de la Universidad Nacional de La Plata, Argentina, durante cinco años a partir del año 2002. Estaba destinado a licenciados y a alumnos avanzados en matemática e informática, y era un curso de postgrado u optativo de grado, según el caso. El Dr. Hernán San Martín fue uno de esos sufridos alumnos. Como prerrequisito se pedían los cursos con contenidos de Álgebra, Lógica y Teoría de Conjuntos que se dictaban en ambas carreras. Los apuntes escritos en esos años fueron el germen de este libro. Estos versaban sobre los cálculos proposicionales Clásico, Intuicionista e Infinitovalente de Łukasiewicz y sus correspondientes contrapartes algebraicas: las álgebras de Boole, las álgebras de Heyting y las MV- algebras. Al empezar a escribir el texto, creímos conveniente agregar temas que nos parecieron útiles para la formación en el área, como dualidades en la teoría de retículos, retículos residuados, ℓ-grupos y sus lógicas. Pretendemos reunir, en castellano y en un nivel accesible, varios temas que usualmente se encuentran dispersos en la literatura. Tratamos de que el texto sea autocontenido y de que se desarrollen los tópicos más abstractos a partir de ejemplos concretos, permitiendo así que la intuición ayude a la comprensión cabal de los conceptos y de su interrelación. Se muestran figuras, diagramas, ejemplos motivadores. Sacrificamos a veces la elegancia de la exposición en aras de hacerla más accesible al estudiante medio. Por ejemplo, se dan elementos de Álgebra Universal en tres etapas de dificultad creciente, en los capítulos 1, 7 y 10, a medida que se van necesitando los contenidos. Asimismo, se suprimen demostraciones muy técnicas y poco conceptuales. Tue, 01 Jan 2019 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/164533 2019-01-01T00:00:00Z Con el propósito de dar una base para el estudio de temas en el área de Álgebra de la Lógica, fue propuesto y dictado por Marta Sagastume el curso "Álgebra del Cálculo Proposicional" en la Facultad de Ciencias Exactas de la Universidad Nacional de La Plata, Argentina, durante cinco años a partir del año 2002. Estaba destinado a licenciados y a alumnos avanzados en matemática e informática, y era un curso de postgrado u optativo de grado, según el caso. El Dr. Hernán San Martín fue uno de esos sufridos alumnos. Como prerrequisito se pedían los cursos con contenidos de Álgebra, Lógica y Teoría de Conjuntos que se dictaban en ambas carreras. Los apuntes escritos en esos años fueron el germen de este libro. Estos versaban sobre los cálculos proposicionales Clásico, Intuicionista e Infinitovalente de Łukasiewicz y sus correspondientes contrapartes algebraicas: las álgebras de Boole, las álgebras de Heyting y las MV- algebras. Al empezar a escribir el texto, creímos conveniente agregar temas que nos parecieron útiles para la formación en el área, como dualidades en la teoría de retículos, retículos residuados, ℓ-grupos y sus lógicas. Pretendemos reunir, en castellano y en un nivel accesible, varios temas que usualmente se encuentran dispersos en la literatura. Tratamos de que el texto sea autocontenido y de que se desarrollen los tópicos más abstractos a partir de ejemplos concretos, permitiendo así que la intuición ayude a la comprensión cabal de los conceptos y de su interrelación. Se muestran figuras, diagramas, ejemplos motivadores. Sacrificamos a veces la elegancia de la exposición en aras de hacerla más accesible al estudiante medio. Por ejemplo, se dan elementos de Álgebra Universal en tres etapas de dificultad creciente, en los capítulos 1, 7 y 10, a medida que se van necesitando los contenidos. Asimismo, se suprimen demostraciones muy técnicas y poco conceptuales. http://sedici.unlp.edu.ar:80/handle/10915/164530 Articulo IV Latin-American Workshop on Cliques in Graphs (Itaipava, Río de Janeiro, Brasil, 16 al 19 de noviembre de 2010); Matemática Contemporânea; vol. 39 An undirected graph G is called an EPT graph if it is the edge intersection graph of a family of paths in a tree. In this paper we de ne the concept of satellite of a clique and we give a necessary condition to be an EPT graph based on satellites of cliques. We characterize the minimal graphs which do not satisfy the previous condition, as a consequence we present a nite family of minimal forbidden subgraphs for the EPT class. Fri, 01 Jan 2010 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/164530 2010-01-01T00:00:00Z An undirected graph G is called an EPT graph if it is the edge intersection graph of a family of paths in a tree. In this paper we de ne the concept of satellite of a clique and we give a necessary condition to be an EPT graph based on satellites of cliques. We characterize the minimal graphs which do not satisfy the previous condition, as a consequence we present a nite family of minimal forbidden subgraphs for the EPT class. http://sedici.unlp.edu.ar:80/handle/10915/162756 Objeto de conferencia XV Congreso Dr. Antonio Monteiro (Bahía Blanca, 5 al 7 de junio de 2019) Un retículo hemi-implicativo es un álgebra (A,∧,∨,→,0,1) de tipo (2,2,2,0,0) tal que (A,∧,∨,0,1) es un retículo distributivo acotado y para toda a,b ∈ A, a → a = 1 y a∧(a →b) ≤ b. [2]. Escribamos hIL para indicar la variedad cuyos elementos son los retículos hemi-implicativos. Las álgebras de semi-Heyting, introducidas por Sankappanavar en [1] como una posible generalización de las álgebras de Heyting, forman una subvariedad propia, SH, de hIL. En esta charla mostraremos que SH se puede caracterizar, alternativamente, como la mayor subvariedad de hIL para la cual el retículo de filtros y el retículo de congruencias de cada elemento son isomorfos. Tue, 01 Jan 2019 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162756 2019-01-01T00:00:00Z Un retículo hemi-implicativo es un álgebra (A,∧,∨,→,0,1) de tipo (2,2,2,0,0) tal que (A,∧,∨,0,1) es un retículo distributivo acotado y para toda a,b ∈ A, a → a = 1 y a∧(a →b) ≤ b. [2]. Escribamos hIL para indicar la variedad cuyos elementos son los retículos hemi-implicativos. Las álgebras de semi-Heyting, introducidas por Sankappanavar en [1] como una posible generalización de las álgebras de Heyting, forman una subvariedad propia, SH, de hIL. En esta charla mostraremos que SH se puede caracterizar, alternativamente, como la mayor subvariedad de hIL para la cual el retículo de filtros y el retículo de congruencias de cada elemento son isomorfos. http://sedici.unlp.edu.ar:80/handle/10915/162725 Preprint SIAM Journal on Discrete Mathematics; vol. 28, no. 3 Graph pebbling is a network optimization model for transporting discrete re- sources that are consumed in transit: the movement of two pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding if a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter two graphs, and that deciding if the pebbling number has a prescribed upper bound is Πᴾ₂ -complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter two graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guaran- tee it, with no characterization in sight. In this paper we investigate an important family of diameter three chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(nᵝ) time, where β = 2ω/(ω + 1) ≅ 1.41 and ω ≅ 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0. Wed, 01 Jan 2014 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162725 2014-01-01T00:00:00Z Graph pebbling is a network optimization model for transporting discrete re- sources that are consumed in transit: the movement of two pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding if a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter two graphs, and that deciding if the pebbling number has a prescribed upper bound is Πᴾ₂ -complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter two graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guaran- tee it, with no characterization in sight. In this paper we investigate an important family of diameter three chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(nᵝ) time, where β = 2ω/(ω + 1) ≅ 1.41 and ω ≅ 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0. http://sedici.unlp.edu.ar:80/handle/10915/162664 Articulo Discussiones Mathematicae Graph Theory; vol. 43, no. 3 This research contains as a main result the proof that every chordal B₁-EPG graph is simultaneously in the graph classes VPT and EPT. In addition, we describe structures that must be present in any B₁-EPG graph which does not admit a Helly-B1-EPG representation. In particular, this paper presents some features of non-trivial families of graphs properly contained in Helly-B₁-EPG, namely bipartite, block, cactus and line graphs of bipartite graphs. Sun, 01 Jan 2023 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162664 2023-01-01T00:00:00Z This research contains as a main result the proof that every chordal B₁-EPG graph is simultaneously in the graph classes VPT and EPT. In addition, we describe structures that must be present in any B₁-EPG graph which does not admit a Helly-B1-EPG representation. In particular, this paper presents some features of non-trivial families of graphs properly contained in Helly-B₁-EPG, namely bipartite, block, cactus and line graphs of bipartite graphs. http://sedici.unlp.edu.ar:80/handle/10915/162604 Articulo Matemática Contemporânea; vol. 39 A complete set of a graph G is a subset of VG whose elements are pairwise adjacent. A clique is a maximal complete set. The clique graph of G, denoted by K(G), is the intersection graph of the family of cliques of G. The clique graph recognition problem asks whether a given graph is a clique graph. This problem was classified recently as NP-complete after being open for 30 years. The complexity of this decision problem is open for very structured and well studied classes of graphs such as planar graphs and chordal graphs. We propose the study of split clique graphs. Fri, 01 Jan 2010 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162604 2010-01-01T00:00:00Z A complete set of a graph G is a subset of VG whose elements are pairwise adjacent. A clique is a maximal complete set. The clique graph of G, denoted by K(G), is the intersection graph of the family of cliques of G. The clique graph recognition problem asks whether a given graph is a clique graph. This problem was classified recently as NP-complete after being open for 30 years. The complexity of this decision problem is open for very structured and well studied classes of graphs such as planar graphs and chordal graphs. We propose the study of split clique graphs. http://sedici.unlp.edu.ar:80/handle/10915/162603 Articulo Discussiones Mathematicae Graph Theory; vol. 43, no. 3 A k-coloring of a graph is neighbor-locating if any two vertices with the same color can be distinguished by the colors of their respective neighbors, that is, the sets of colors of their neighborhoods are different. The neighbor- locating chromatic number χNL(G) is the minimum k such that a neighbor- locating k-coloring of G exists. In this paper, we give upper and lower bounds on the neighbor-locating chromatic number in terms of the order and the degree of the vertices for unicyclic graphs and trees. We also obtain tight upper bounds on the order of trees and unicyclic graphs in terms of the neighbor-locating chromatic number. Further partial results for trees are also established. Sun, 01 Jan 2023 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162603 2023-01-01T00:00:00Z A k-coloring of a graph is neighbor-locating if any two vertices with the same color can be distinguished by the colors of their respective neighbors, that is, the sets of colors of their neighborhoods are different. The neighbor- locating chromatic number χNL(G) is the minimum k such that a neighbor- locating k-coloring of G exists. In this paper, we give upper and lower bounds on the neighbor-locating chromatic number in terms of the order and the degree of the vertices for unicyclic graphs and trees. We also obtain tight upper bounds on the order of trees and unicyclic graphs in terms of the neighbor-locating chromatic number. Further partial results for trees are also established. http://sedici.unlp.edu.ar:80/handle/10915/162597 Articulo Matemática Contemporânea; vol. 46 The t-pebbling number is the smallest integer m so that any initially distributed supply of m pebbles can place t pebbles on any target vertex via pebbling moves. The 1-pebbling number of diameter 2 graphs is well-studied. Here we investigate the t-pebbling number of diameter 2 graphs under the lens of connectivity. Mon, 01 Jan 2018 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162597 2018-01-01T00:00:00Z The t-pebbling number is the smallest integer m so that any initially distributed supply of m pebbles can place t pebbles on any target vertex via pebbling moves. The 1-pebbling number of diameter 2 graphs is well-studied. Here we investigate the t-pebbling number of diameter 2 graphs under the lens of connectivity. http://sedici.unlp.edu.ar:80/handle/10915/162540 Articulo Electronic Notes in Discrete Mathematics; vol. 44 Basic chordal graphs arose when comparing clique trees of chordal graphs and compatible trees of dually chordal graphs. They were defined as those chordal graphs whose clique trees are exactly the compatible trees of its clique graph. In this work, we consider some subclasses of basic chordal graphs, like hereditary basic chordal graphs, basic DV and basic RDV graphs, we characterize them and we find some other properties they have, mostly involving clique graphs. Fri, 01 Nov 2013 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162540 2013-11-01T00:00:00Z Basic chordal graphs arose when comparing clique trees of chordal graphs and compatible trees of dually chordal graphs. They were defined as those chordal graphs whose clique trees are exactly the compatible trees of its clique graph. In this work, we consider some subclasses of basic chordal graphs, like hereditary basic chordal graphs, basic DV and basic RDV graphs, we characterize them and we find some other properties they have, mostly involving clique graphs. http://sedici.unlp.edu.ar:80/handle/10915/162534 Articulo Electronic Notes in Discrete Mathematics; vol. 37 Let G be the class of all graphs and K the clique operator. The validity of the equality K(G) = K²(G) has been an open question for several years. A graph in K(G) but not in K²(G) is exhibited here. Mon, 01 Aug 2011 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162534 2011-08-01T00:00:00Z Let G be the class of all graphs and K the clique operator. The validity of the equality K(G) = K²(G) has been an open question for several years. A graph in K(G) but not in K²(G) is exhibited here. http://sedici.unlp.edu.ar:80/handle/10915/162528 Articulo Electronic Notes in Discrete Mathematics; vol. 37 Chordal and dually chordal graphs possess characteristic tree representations, namely, clique trees and compatible trees, respectively. The following problem is studied: given a chordal graph G, it has to be determined if the clique trees of G are exactly the compatible trees of K(G). This does not always happen. A necessary and sufficient condition so that it is true, in terms of the minimal vertex separators of the graph, is found. Mon, 01 Aug 2011 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162528 2011-08-01T00:00:00Z Chordal and dually chordal graphs possess characteristic tree representations, namely, clique trees and compatible trees, respectively. The following problem is studied: given a chordal graph G, it has to be determined if the clique trees of G are exactly the compatible trees of K(G). This does not always happen. A necessary and sufficient condition so that it is true, in terms of the minimal vertex separators of the graph, is found. http://sedici.unlp.edu.ar:80/handle/10915/162385 Articulo Electronic Notes in Discrete Mathematics; vol. 35 Many works related to dually chordal graphs, their cliques and neighborhoods were published. We will undertake a similar study but by considering minimal separators and their properties. Moreover we find new characterizations of dually chordal graphs. Tue, 01 Dec 2009 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162385 2009-12-01T00:00:00Z Many works related to dually chordal graphs, their cliques and neighborhoods were published. We will undertake a similar study but by considering minimal separators and their properties. Moreover we find new characterizations of dually chordal graphs. http://sedici.unlp.edu.ar:80/handle/10915/162382 Articulo Discrete Mathematics; vol. 340, no. 7 Graph pebbling is a network model for transporting discrete resources that are consumed in transit. Deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter two graphs, and deciding whether the pebbling number has a prescribed upper bound is Πᴾ₂-complete. Recently we proved that the pebbling number of a split graph can be computed in polynomial time. This paper advances the program of finding other polynomial classes, moving away from the large tree width, small diameter case (such as split graphs) to small tree width, large diameter, continuing an investigation on the important subfamily of chordal graphs called k-trees. In particular, we provide a formula, that can be calculated in polynomial time, for the pebbling number of any semi-2-tree, falling shy of the result for the full class of 2-trees. Sat, 01 Jul 2017 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/162382 2017-07-01T00:00:00Z Graph pebbling is a network model for transporting discrete resources that are consumed in transit. Deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter two graphs, and deciding whether the pebbling number has a prescribed upper bound is Πᴾ₂-complete. Recently we proved that the pebbling number of a split graph can be computed in polynomial time. This paper advances the program of finding other polynomial classes, moving away from the large tree width, small diameter case (such as split graphs) to small tree width, large diameter, continuing an investigation on the important subfamily of chordal graphs called k-trees. In particular, we provide a formula, that can be calculated in polynomial time, for the pebbling number of any semi-2-tree, falling shy of the result for the full class of 2-trees. http://sedici.unlp.edu.ar:80/handle/10915/159867 Articulo Electronic Notes in Theoretical Computer Science; vol. 346 This paper is inspired in the well known characterization of chordal graphs as the intersection graphs of subtrees of a tree. We consider families of induced trees of any graph and we prove that their recognition is NP-Complete. A consequence of this fact is that the concept of clique tree of chordal graphs cannot be widely generalized. Finally, we consider the fact that every graph is the intersection graph of induced trees of a bipartite graph and we characterize some classes that arise when we impose restrictions on the host bipartite graph. Tue, 01 Jan 2019 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/159867 2019-01-01T00:00:00Z This paper is inspired in the well known characterization of chordal graphs as the intersection graphs of subtrees of a tree. We consider families of induced trees of any graph and we prove that their recognition is NP-Complete. A consequence of this fact is that the concept of clique tree of chordal graphs cannot be widely generalized. Finally, we consider the fact that every graph is the intersection graph of induced trees of a bipartite graph and we characterize some classes that arise when we impose restrictions on the host bipartite graph. http://sedici.unlp.edu.ar:80/handle/10915/156340 Articulo Revista de la Unión Matemática Argentina; vol. 61, no. 1 We consider elliptic equations of order 2m with Hölder coefficients. We show local solvability of the Dirichlet problem with m conditions on the boundary of the upper half space. First we consider local solvability in free space and then we treat the boundary case. Our method is based on applying the operator to an approximate solution and iterating in the Hölder spaces. A priori estimates for the approximate solution is the essential part of the paper. Wed, 01 Jan 2020 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/156340 2020-01-01T00:00:00Z We consider elliptic equations of order 2m with Hölder coefficients. We show local solvability of the Dirichlet problem with m conditions on the boundary of the upper half space. First we consider local solvability in free space and then we treat the boundary case. Our method is based on applying the operator to an approximate solution and iterating in the Hölder spaces. A priori estimates for the approximate solution is the essential part of the paper. http://sedici.unlp.edu.ar:80/handle/10915/156339 Articulo Revista de la Unión Matemática Argentina; vol. 58, no. 2 We consider 2mth order elliptic equations with Hölder coefficients in half space. We solve the Dirichlet problem with m conditions on the boundary of the upper half space. We fi rst analyze the constant coefficient case, finding the Green function and a representation formula, and then prove Schauder estimates. Sun, 01 Jan 2017 00:00:00 GMT http://sedici.unlp.edu.ar:80/handle/10915/156339 2017-01-01T00:00:00Z We consider 2mth order elliptic equations with Hölder coefficients in half space. We solve the Dirichlet problem with m conditions on the boundary of the upper half space. We fi rst analyze the constant coefficient case, finding the Green function and a representation formula, and then prove Schauder estimates.