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http://hdl.handle.net/2117/3178
20150706T22:40:17Z

Almost every tree with m edges decomposes K2m,2m
http://hdl.handle.net/2117/28488
Title: Almost every tree with m edges decomposes K2m,2m
Authors: Drmota, Michael; Lladó Sánchez, Ana M.
Abstract: We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size. © Cambridge University Press 2013.
20150701T11:06:35Z

Classification of numerical 3semigroups by means of Lshapes
http://hdl.handle.net/2117/28487
Title: Classification of numerical 3semigroups by means of Lshapes
Authors: Aguiló Gost, Francisco de Asis L.; Marijuan López, Carlos
Abstract: We recall Lshapes, which are minimal distance diagrams, related to weighted 2Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate Lshapes to each numerical 3semigroup and we describe some main invariants of numerical 3semigroups in terms of their associated Lshapes. Finally, we give a characterization of the parameters of the Lshapes associated with a numerical 3semigroup in terms of its generators, and we use it to classify the numerical 3semigroups of interest in curve singularity.
20150701T11:02:05Z

On global locationdomination in bipartite graphs
http://hdl.handle.net/2117/28318
Title: On global locationdomination in bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
20150616T09:42:50Z

On global locationdomination in graphs
http://hdl.handle.net/2117/28254
Title: On global locationdomination in graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating set S of a graph G is called locatingdominating, LDset for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locatingdominating sets of minimum cardinality are called LDcodes and the cardinality of an LDcode is the locationdomination number lambda(G). An LDset S of a graph G is global if it is an LDset of both G and its complement G'. The global locationdomination number lambda g(G) is introduced as the minimum cardinality of a global LDset of G.
In this paper, some general relations between LDcodes and the locationdomination number in a graph and its complement are presented first.
Next, a number of basic properties involving the global locationdomination number are showed. Finally, both parameters are studied indepth for the family of blockcactus graphs.
20150610T11:51:21Z

Oxidative stress is a central target for physical exercise neuroprotection against pathological brain aging
http://hdl.handle.net/2117/27948
Title: Oxidative stress is a central target for physical exercise neuroprotection against pathological brain aging
Authors: GarciaMesa, Yoelvis; Colie, Sandra; Corpas, Ruben; Cristofol, Rosa; Comellas Padró, Francesc de Paula; Nebreda, Angel; GiménezLlort, Lydia; Sanfeliu, Coral
Abstract: Physical exercise is suggested for preventing or delaying senescence and Alzheimer’s disease (AD). We have examined its therapeutic value in the advanced stage of ADlike pathology in 3xTgAD female mice through voluntary wheel running from 12 to 15 months of age. Mice submitted to exercise showed improved body fitness, immunorejuvenation, improvement of behavior and cognition, and reduced amyloid and tau pathology. Brain tissue analysis of aged 3xTgAD mice showed high levels of oxidative damage. However, this damage was decreased by physical exercise through regulation of redox homeostasis. Network analyses showed that oxidative stress was a central event, which correlated with ADlike pathology and the ADrelated behaviors of anxiety, apathy, and cognitive loss. This study corroborates the importance of redox mechanisms in the neuroprotective effect of physical exercise, and supports the theory of the crucial role of oxidative stress in the switch from normal brain aging to pathological aging and AD.
20150518T12:01:12Z

Decomposing almost complete graphs by random trees
http://hdl.handle.net/2117/27908
Title: Decomposing almost complete graphs by random trees
Authors: Lladó Sánchez, Ana M.
Abstract: An old conjecture of Ringel states that every tree with m edges decom poses the complete graph K 2 m +1 . A more general version of the Ringel’s conjecture says that every tree with m edges decomposes K rm +1 for each r = 2 provided that r and m + 1 are not both odd. The best lower bound for the order of a complete graph decomposed by a given tree with m edge is O ( m 3 ). We show that asymptotically almost surely a random tree with m edges and p = 2 m + 1 is a prime decomposes the complete graph minus one edge K 3 p  e . We also show that, for every prime of the form 2 km + 1 a random tree with m edges asymptotically almost surely decomposes the graph K 2 km +1 (3) obtained from the complete graph by replacing each vertex by the complement of a triangle.
20150513T11:30:43Z

A new application of the $\otimes_h$product to $\alpha$labelings
http://hdl.handle.net/2117/27897
Title: A new application of the $\otimes_h$product to $\alpha$labelings
Authors: López Masip, Susana Clara; Muntaner Batle, Francesc Antoni
Abstract: The weak tensor product was introduced by Snevily as a way to construct new graphs that admit alabelings from a pair of known agraphs. In this article, we show that this product and the application to alabelings can be generalized by considering as a second factor of the product, a family G of bipartite (p, q)graphs, p and q fixed. The only additional restriction that we should consider is that for every F ¿ G , there exists an alabeling fF with fF (V(F )) = L¿H, where L, H ¿ [0, q] are the stable sets induced by the characteristic of fF and they do not depend on F .Wealso obtain analogous applications to near alabelings and bigraceful labelings.
20150512T11:53:58Z

Caracterizaciones combinatorias y algebraicas de grafos distanciaregulares
http://hdl.handle.net/2117/27894
Title: Caracterizaciones combinatorias y algebraicas de grafos distanciaregulares
Authors: Fiol Mora, Miquel Àngel
Abstract: Los grafos distanciaregulares aparecen a menudo en el estudio de es
tructuras matemáticas con un alto grado de simetría y/o regularidad. Un ejemplo bien conocido de tales grafos son los esqueletos de los sólidos platónicos. Desde que fueron propuestos por Norman Biggs, los grafos distanciaregulares han sido caracterizados por numerosos resultados, tanto de carácter combinatorio como algebraico. Como ejemplo del primer caso, sabemos que un grafo es distanciaregular si, y sólo si, el número de caminos de una longitud dada entre dos vértices sólo depende de la distancia entre dichos vértices. En esta charla se van a presentar y comparar las diferentes caracterizaciones conocidas, tanto las más clásicas como las que han sido recientemente descubiertas por el conferenciante y algunos de sus colaboradores. Entre las últimas, cabe destacar el que ya es conocido en la literatura com el `teorema del exceso espectral’. Este resultado puede considerarse como una caracterización casiespectral, y afirma que un grafo es distanciaregular si, y sólo si, su exceso espectral (una cantidad calculable a partir de su matriz de adyacencia) es igual a su exceso medio (el número medio de vértices a distancia máxima de cada vértice).
20150512T11:41:00Z

An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs
http://hdl.handle.net/2117/27893
Title: An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs
Authors: Abiad, Aida; Fiol Mora, Miquel Àngel; Haemers, Willem H.; Perarnau Llobet, Guillem
Abstract: We apply eigenvalue interlacing techniques for obtaining lower and upper
bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality.
This leads to generalizations of, and variations on theorems by Grone, and Grone &
Merris. As a consequence we obtain inequalities involving bounds for some wellknown
parameters of a graph, such as edgeconnectivity, and the isoperimetric number.
20150512T11:31:57Z

Some results on the structure of multipoles in the study of snarks
http://hdl.handle.net/2117/27888
Title: Some results on the structure of multipoles in the study of snarks
Authors: Fiol Mora, Miquel Àngel; Vilaltella Castanyer, Joan
Abstract: Multipoles are the pieces we obtain by cutting some edges of a cubic graph in one or more points. As a result of the cut, a multipole M has vertices attached to a dangling edge with one free end, and isolated edges with two free ends. We refer to such free ends as semiedges, and to isolated edges as free edges. Every 3edgecoloring of a multipole induces a coloring or state of its semiedges, which satisfies the Parity Lemma. Multipoles have been extensively used in the study of snarks, that is, cubic graphs which are not 3edgecolorable. Some results on the states and structure of the socalled color complete and color closed multipoles are presented. In particular, we give lower and upper linear bounds on the minimum order of a color complete multipole, and compute its exact number of states. Given two multipoles M1 and M2 with the same number of semiedges, we say that M1 is reducible to M2 if the state set of M2 is a nonempty subset of the state set of M1 and M2 has less vertices than M1. The function v(m) is defined as the maximum number of vertices of an irreducible multipole with rn semiedges. The exact values of v(m) are only known for m <= 5. We prove that tree and cycle multipoles are irreducible and, as a byproduct, that v(m) has a linear lower bound.
20150512T10:08:14Z

Approximate results for rainbow labelings
http://hdl.handle.net/2117/27843
Title: Approximate results for rainbow labelings
Authors: Lladó Sánchez, Ana M.
Description: Article de recerca
20150508T11:21:05Z

On starforest ascending subgraph decomposition
http://hdl.handle.net/2117/27841
Title: On starforest ascending subgraph decomposition
Authors: Aroca Farrerons, José María; Lladó Sánchez, Ana M.
20150508T11:15:42Z

Decomposing almost complete graphs by random trees
http://hdl.handle.net/2117/27840
Title: Decomposing almost complete graphs by random trees
Authors: Lladó Sánchez, Ana M.
20150508T11:13:27Z

Magic coverings and the Kronecker product
http://hdl.handle.net/2117/27818
Title: Magic coverings and the Kronecker product
Authors: López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
Abstract: In this paper we study a relationship existing among (super) magic coverings and the well known Kronecker product of matrices. We also introduce the concept of Z(n)property for digraphs in order to study this relation mentioned before. The results obtained in this paper can also be applied to construct Smagic partitions.
20150507T11:53:47Z

On perfect and quasiperfect domination in graphs
http://hdl.handle.net/2117/27709
Title: On perfect and quasiperfect domination in graphs
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M Luz
20150504T10:26:03Z