Edge-superconnectivity of semiregular cages with odd girth

A graph is said to be edge-superconnected if each minimum edge-cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a {d, d + 1}- semiregular graph if all its vertices have degree either d or d+1. A smallest {d,d+1}-semiregular graph G with girth g is said to be a ({d, d+1}; g)-cage.We show that every ({d, d+1}; g)-cage with odd girth g is edge-superconnected.Peer Reviewe

Vertex-disjoint cycles in bipartite tournaments

Let k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.Peer ReviewedPostprint (author's final draft

Bounds on the k-restricted arc connectivity of some bipartite tournaments

For k¿=¿2, a strongly connected digraph D is called -connected if it contains a set of arcs W such that contains at least k non-trivial strong components. The k-restricted arc connectivity of a digraph D was defined by Volkmann as . In this paper we bound for a family of bipartite tournaments T called projective bipartite tournaments. We also introduce a family of “good” bipartite oriented digraphs. For a good bipartite tournament T we prove that if the minimum degree of T is at least then where N is the order of the tournament. As a consequence, we derive better bounds for circulant bipartite tournaments.Peer ReviewedPostprint (author's final draft

Friendship conceptions: an exploratory study with spanish and immigrant children established in the Madrid Community

El objetivo de nuestro estudio es conocer la concepción que tienen los niños acerca de la amistad, viendo si ésta varía en función del género y las características culturales de los participantes. Para ello, se elaboró una entrevista semiestructurada de respuesta abierta, que se aplicó –siguiendo el método clínico propuesto por Piaget–, a una muestra de 30 estudiantes (16 niñas y 14 niños) de 5º y 6º de Educación Primaria, con un rango de edad que oscilaba entre los 11;1 y 12;3 años, y donde el 50% eran inmigrantes y la parte restante españoles (autóctonos). Los resultados de este trabajo indican que no hay diferencias significativas en la concepción que tienen los niños de la amistad según su origen nacional, entendiéndola como un vínculo que se basa en la ayuda, la confianza, la compañía y la fidelidad. Sin embargo, se encontraron diferencias significativas en cuanto a la facilidad a la hora de entablar relaciones con los iguales, y el origen étnico de las amistades, asegurando los españoles, en mayor medida que los inmigrantes, que les costaba hacer amigos, y que éstos eran en su mayoría de origen español. Igualmente, se hallaron diferencias significativas en función del género, destacando las niñas en mayor medida que los niños, la confianza como el rasgo que diferencia a los amigos, del resto de iguales que no lo son.The aim of our study is to know the childrens’ conceptions of friendship and looking at if it changes according to gender and the cultural characteristics of the participants. To this end, a semistructured interview of open answerered questions was developed, and applied –following the piagetian method– to a sample of 30 students (16 girls and 14 boys) of the 5th and 6th grades of primary school. The ages of the children varied between 11;1 and 12;3 years, and the 50% were immigrants, with the remaining part being natives Spaniards. The results of this work show that there aren’t significant differences in the childrens’ conceptions of friendship based on their national origin, understanding it as a link based on help, confidence, company and faithfulness. However, significant differences were found in relation to the ease of starting relationships with the peers, and the ethnical origin of their friends, confirming a higher number of Spanish natives that had the most problems making friends, as opposed to the immigrants, and whose friends were mostly Spanish natives. Likewise, significant differences were found according to gender, pointing out that the girls, rather than boys, found confidence as a trait that differentiated their friends from the rest of their peers.peerReviewe