An advance in infinite graph models for the analysis of transportation networks

This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite’ graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation of dangerous goods are presented; they involve the analysis of networks and percolation thresholds.Unión Europea FEDER G-GI3003/IDI

The Size of a Graph Without Topological Complete Subgraphs

In this note we show a new upperbound for the function ex(n;TKp), i.e., the maximum number of edges of a graph of order n not containing a subgraph homeomorphic to the complete graph of order p. Further, for ${\left \lceil \frac{2n+5}{3}\right \rceil}\leq p < n$ we provide exact values for this function

Extremal Graphs without Topological Complete Subgraphs

The exact values of the function $ex(n;TK_{p})$ are known for ${\lceil \frac{2n+5}{3}\rceil}\leq p < n$ (see [Cera, Diánez, and Márquez, SIAM J. Discrete Math., 13 (2000), pp. 295--301]), where $ex(n;TK_p)$ is the maximum number of edges of a graph of order n not containing a subgraph homeomorphic to the complete graph of order $p.$ In this paper, for ${\lceil \frac{2n+6}{3} \rceil}\leq p < n - 3,$ we characterize the family of extremal graphs $EX(n;TK_{p}),$ i.e., the family of graphs with n vertices and $ex(n;TK_{p})$ edges not containing a subgraph homeomorphic to the complete graph of order $p.

Superconnectivity of Networks Modeled by the Strong Product of Graphs

Maximal connectivity and superconnectivity in a network are two important features of its reliability. In this paper, using graph terminology, we first give a lower bound for the vertex connectivity of the strong product of two networks and then we prove that the resulting structure is more reliable than its generators. Namely, sufficient conditions for a strong product of two networks to be maximally connected and superconnected are given.Ministerio de Economía y Competitividad MTM2014-60127-

On the Ramsey numbers for stars versus complete graphs

For graphs G1, . . . , Gs, the multicolor Ramsey number R(G1, . . . , Gs) is the smallest integer r such that if we give any edge col-oring of the complete graph on r vertices with s colors then there exists a monochromatic copy of Gi colored with color i, for some 1 ≤ i ≤ s. In this work the multicolor Ramsey number R(Kp1 , . . . , Kpm , K1,q1 , . . . , K1,qn ) is determined for any set of com-plete graphs and stars in terms of R(Kp1 , . . . , Kpm )Ministerio de Educación y Ciencia MTM2008-06620-C03-02Junta de Andalucía P06-FQM-0164

Subdivisions in a bipartite graph

Given a bipartite graph G with m and n vertices, respectively,in its vertices classes, and given two integers s, t such that 2 ≤ s ≤ t, 0 ≤ m−s ≤ n−t, and m+n ≤ 2s+t−1, we prove that if G has at least mn−(2(m−s)+n−t) edges then it contains a subdivision of the complete bipartite $K_(s,t)$ with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn − (2(m − s) + n − t + 1) edges for this topological Turan type problem.Peer Reviewe

Avances en Matemática Discreta en Andalucía. V Encuentro andaluz de Matemática Discreta. La Línea de la Concepción (Cádiz), 4-5 de julio de 2007

V Encuentro andaluz de Matemática Discreta. La Línea de la Concepción (Cádiz), 4-5 de julio de 200

Development of Emotional Intelligence through Physical Activity and Sport Practice. A Systematic Review

At present, knowledge of physical and cognitive aspects is essential in the sporting context. Faced with this situation, the control and knowledge of emotions has a person on himself and on others, affects the sporting action. The aim of this work is to examine the relationship between emotional intelligence and the practice of physical activity. Through a systematic review in databases such as the Web of Science and Scopus that contain the terms of emotional intelligence along with the parameters of physical activity and sport. Twenty-four articles comprised the sample for further analysis. By way of conclusion it can be said that the main field of study of emotional intelligence related to the practice of physical activity is educational. Likewise, emotional intelligence is a determining factor in the improvement of sports competences.This research was funded by Spanish Ministry of Education grant number FPU16/03114

El tamaño de un grafo sin subgrafos homeomorfos a un grafo completo

"Desde el origen de la Teoría de Grafos Extremales, uno de los problemas más generales que pueden plantearse en este campo, es estudiar los grafos de manera que podamos encontrar condiciones para que contengan o no a un subgrafo dado. Es en este sentido donde podemos encuadrar los objetivos de esta Tesis.Concretamente, nos va interesar el estudio de la función ex (n; TKp), es decir, el número máximo de aristas de un grafo de orden n para que no contenga a un subgrafo homeomorfo al grafo completo de orden p. A su vez, como en todo problema extremal, resulta interesante caracterizar los grafos maximales para la propiedad anterior, esto es lo que se conoce como familia de grafos extremales. Una pequeña variación del problema anterior nos conduce al análisis paralelo de la función ex (n; TK-p).Por otra parte, el estudio de problemas extremales, como los anteriores descritos, cuando el orden de los grafos estudiados es suficientemente grande, conduce de forma natural a plantearse el problema para grafos infinitos. Claro está, que para grafos infinitos, carece de sentido estudiar el número de aristas frente al número de vértices por ser, en general, ambos infinitos. Intentamos dar solución a este problema introduciendo el concepto de valencia media de un grafo infinito como límite de las valencias medias de una sucesión creciente de grafos finitos que lo recubren. Esto, nos permite abordar el problema extremal, relacionado con la contención de subgrafos homeomorfos a un grafo completo, para grafos infinitos en función de la valencia media, así como, establecer las relaciones con el correspondiente problema para el caso finito.