Capítols de llibre
http://hdl.handle.net/2117/3183
Tue, 01 Dec 2015 13:16:38 GMT2015-12-01T13:16:38Zc-Critical graphs with maximum degree three
http://hdl.handle.net/2117/76780
c-Critical graphs with maximum degree three
Fiol Mora, Miquel Àngel
Let $G$ be a (simple) gtoph with maximum degree three and
chromatic index four. A 3-edge-coloring of G is a coloring of
its edges in which only three colors are used. Then a vertex is
conflicting when some edges incident to it have the same color.
The minimum possible number of conflicting vertices that a 3-
edge-coloring of G can have is called the edge-coloring degree,
$d(G)$, of $G$. Here we are mainly interested in the structure of a
graph $G$ with given edge-coloring degree and, in particula.r, when
G is c-critical, that is $d(G) = c \ge 1$ and $d(G - e) < c$ for any
edge $e$ of $G$.
Tue, 15 Sep 2015 08:25:28 GMThttp://hdl.handle.net/2117/767802015-09-15T08:25:28ZFiol Mora, Miquel ÀngelLet $G$ be a (simple) gtoph with maximum degree three and
chromatic index four. A 3-edge-coloring of G is a coloring of
its edges in which only three colors are used. Then a vertex is
conflicting when some edges incident to it have the same color.
The minimum possible number of conflicting vertices that a 3-
edge-coloring of G can have is called the edge-coloring degree,
$d(G)$, of $G$. Here we are mainly interested in the structure of a
graph $G$ with given edge-coloring degree and, in particula.r, when
G is c-critical, that is $d(G) = c \ge 1$ and $d(G - e) < c$ for any
edge $e$ of $G$.An algebraic model for the storage of data in parallel memories
http://hdl.handle.net/2117/27169
An algebraic model for the storage of data in parallel memories
Fiol Mora, Miquel Àngel; Serra Albó, Oriol
The use of SIMD computers requires efficient schemes of storage of data in order to have conflict-free acces in parallel computation. In this paper we restate the problem of finding such chemes in an algebraic context. This approach supplies simple statements and proofs of main results on the subject, and allows further development of it.
Wed, 08 Apr 2015 12:44:38 GMThttp://hdl.handle.net/2117/271692015-04-08T12:44:38ZFiol Mora, Miquel ÀngelSerra Albó, OriolThe use of SIMD computers requires efficient schemes of storage of data in order to have conflict-free acces in parallel computation. In this paper we restate the problem of finding such chemes in an algebraic context. This approach supplies simple statements and proofs of main results on the subject, and allows further development of it.Connectivity: properties and structure
http://hdl.handle.net/2117/22004
Connectivity: properties and structure
Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel
Connectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, such as Menger’s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson’s theorem about flows and Hall’s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and fault-tolerant interconnection or communication networks.
Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66].
Wed, 12 Mar 2014 12:00:55 GMThttp://hdl.handle.net/2117/220042014-03-12T12:00:55ZBalbuena Martínez, Maria Camino TeófilaFàbrega Canudas, JoséFiol Mora, Miquel ÀngelConnectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, such as Menger’s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson’s theorem about flows and Hall’s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and fault-tolerant interconnection or communication networks.
Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66].Further topics in connectivity
http://hdl.handle.net/2117/22000
Further topics in connectivity
Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel
Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results concerning maximal (vertex- or edge-) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the so-called “conditional connectivity,” are considered.
For unexplained terminology concerning connectivity, see §4.1.
Wed, 12 Mar 2014 11:17:54 GMThttp://hdl.handle.net/2117/220002014-03-12T11:17:54ZBalbuena Martínez, Maria Camino TeófilaFàbrega Canudas, JoséFiol Mora, Miquel ÀngelContinuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results concerning maximal (vertex- or edge-) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the so-called “conditional connectivity,” are considered.
For unexplained terminology concerning connectivity, see §4.1.Locating domination in graphs and their complements
http://hdl.handle.net/2117/21284
Locating domination in graphs and their complements
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A dominating set
S
of a graph
G
is called
locating-dominating
,
LD-set
for
short, if every vertex
v
not in
S
is uniquely determined by the set of neighbors of
v
belonging to
S
. Locating-dominating sets of minimum cardinality are called
LD
-codes
and the cardinality of an LD-code is the
location-domination number
. An LD-set of a
graph
G
is
global
if
S
is an LD-set of both
G
and its complement,
G
. In this work, we give
some relations between the locating-dominating sets and location-domination number in
a graph and its complement
Mon, 20 Jan 2014 12:49:27 GMThttp://hdl.handle.net/2117/212842014-01-20T12:49:27ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA dominating set
S
of a graph
G
is called
locating-dominating
,
LD-set
for
short, if every vertex
v
not in
S
is uniquely determined by the set of neighbors of
v
belonging to
S
. Locating-dominating sets of minimum cardinality are called
LD
-codes
and the cardinality of an LD-code is the
location-domination number
. An LD-set of a
graph
G
is
global
if
S
is an LD-set of both
G
and its complement,
G
. In this work, we give
some relations between the locating-dominating sets and location-domination number in
a graph and its complementAula virtual de soporte a la docencia y al autoaprendizaje del cálculo para estudiantes universitarios con material docente y aplicaciones basadas en software libre
http://hdl.handle.net/2117/19014
Aula virtual de soporte a la docencia y al autoaprendizaje del cálculo para estudiantes universitarios con material docente y aplicaciones basadas en software libre
Jarauta Bragulat, Eusebio; Pelayo Melero, Ignacio Manuel
Fri, 26 Apr 2013 12:40:48 GMThttp://hdl.handle.net/2117/190142013-04-26T12:40:48ZJarauta Bragulat, EusebioPelayo Melero, Ignacio ManuelPolynomials in finite geometry
http://hdl.handle.net/2117/18848
Polynomials in finite geometry
Ball, Simeon Michael; Blokhuis, Aart
Wed, 17 Apr 2013 10:13:03 GMThttp://hdl.handle.net/2117/188482013-04-17T10:13:03ZBall, Simeon MichaelBlokhuis, AartThe polynomial method in Galois geometries
http://hdl.handle.net/2117/18846
The polynomial method in Galois geometries
Ball, Simeon Michael
The polynomial method refers to the application of polynomials to combinatorial
problems. The method is particularly effective for Galois geometries and a number
of problems and conjectures have been solved using the polynomial method. In many
cases the polynomial approach is the only method which we know of that works. In this
article, the various polynomial techniques that have been applied to Galois geometries
are detailed and, to demonstrate how to apply these techniques, some of the problems
referred to above are resolved.
Wed, 17 Apr 2013 09:56:10 GMThttp://hdl.handle.net/2117/188462013-04-17T09:56:10ZBall, Simeon MichaelThe polynomial method refers to the application of polynomials to combinatorial
problems. The method is particularly effective for Galois geometries and a number
of problems and conjectures have been solved using the polynomial method. In many
cases the polynomial approach is the only method which we know of that works. In this
article, the various polynomial techniques that have been applied to Galois geometries
are detailed and, to demonstrate how to apply these techniques, some of the problems
referred to above are resolved.Aprendizaje colaborativo en base a problemas mediante el uso del foro electrónico
http://hdl.handle.net/2117/18165
Aprendizaje colaborativo en base a problemas mediante el uso del foro electrónico
Buenestado Caballero, Pablo; Minelli de Oliveira, Janaina; Moragas Gascons, Lluís; Rodríguez Pérez, Ana Carmen; Cañadas Lorenzo, Juan Carlos; Pelayo Melero, Ignacio Manuel
La incorporación de las plataformas digitales en la educación impulsa nuevas maneras de aprender. La universidad promueve la participación sincrónica y asincrónica entre sujetos que no están en el mismo lugar, ni al mismo tiempo.
Una de las herramientas tecnológicas que favorece la interacción a distancia y asincrónica es el Foro Virtual, herramienta que ayuda a compartir reflexiones y búsquedas favoreciendo, al mismo tiempo, el desarrollo de habilidades sociales y la mejora de la comunicación escrita. La relación en el Foro refuerza el aprendizaje de los individuos.
El objetivo de esta comunicación es presentar un método eficiente para que un estudiante aprenda en colaboración con el grupo de compañeros mediante la resolución de problemas, el análisis y la crítica interactiva usando el foro electrónico de la plataforma digital.
Mon, 11 Mar 2013 10:26:43 GMThttp://hdl.handle.net/2117/181652013-03-11T10:26:43ZBuenestado Caballero, PabloMinelli de Oliveira, JanainaMoragas Gascons, LluísRodríguez Pérez, Ana CarmenCañadas Lorenzo, Juan CarlosPelayo Melero, Ignacio ManuelLa incorporación de las plataformas digitales en la educación impulsa nuevas maneras de aprender. La universidad promueve la participación sincrónica y asincrónica entre sujetos que no están en el mismo lugar, ni al mismo tiempo.
Una de las herramientas tecnológicas que favorece la interacción a distancia y asincrónica es el Foro Virtual, herramienta que ayuda a compartir reflexiones y búsquedas favoreciendo, al mismo tiempo, el desarrollo de habilidades sociales y la mejora de la comunicación escrita. La relación en el Foro refuerza el aprendizaje de los individuos.
El objetivo de esta comunicación es presentar un método eficiente para que un estudiante aprenda en colaboración con el grupo de compañeros mediante la resolución de problemas, el análisis y la crítica interactiva usando el foro electrónico de la plataforma digital.Characterizing tractability by tissue-like P-systems
http://hdl.handle.net/2117/16563
Characterizing tractability by tissue-like P-systems
Rius Font, Miquel; Gutiérrez Escudero, Rosa; Pérez Jiménez, Mario J.
In the framework of recognizer cell–like membrane systems
it is well known that the construction of exponential number of objects
in polynomial time is not enough to efficiently solve NP–complete problems.
Nonetheless, it may be sufficient to create an exponential number
of membranes in polynomial time.
In this paper, we study the computational efficiency of recognizer tissue
P systems with communication (symport/antiport) rules and division
rules. Some results have been already obtained in this direction: (a) using
communication rules and making no use of division rules, only tractable
problems can be efficiently solved; (b) using communication rules with
length three and division rules, NP–complete problems can be efficiently
solved. In this paper, we show that the length of communication rules
plays a relevant role from the efficiency point of view for this kind of P
systems.
Tue, 25 Sep 2012 12:13:20 GMThttp://hdl.handle.net/2117/165632012-09-25T12:13:20ZRius Font, MiquelGutiérrez Escudero, RosaPérez Jiménez, Mario J.In the framework of recognizer cell–like membrane systems
it is well known that the construction of exponential number of objects
in polynomial time is not enough to efficiently solve NP–complete problems.
Nonetheless, it may be sufficient to create an exponential number
of membranes in polynomial time.
In this paper, we study the computational efficiency of recognizer tissue
P systems with communication (symport/antiport) rules and division
rules. Some results have been already obtained in this direction: (a) using
communication rules and making no use of division rules, only tractable
problems can be efficiently solved; (b) using communication rules with
length three and division rules, NP–complete problems can be efficiently
solved. In this paper, we show that the length of communication rules
plays a relevant role from the efficiency point of view for this kind of P
systems.