Tight lower bounds on the number of bicliques in false-twin-free graphs

A \emph{biclique} is a maximal bipartite complete induced subgraph of $G$. Bicliques have been studied in the last years motivated by the large number of applications. In particular, enumeration of the maximal bicliques has been of interest in data analysis. Associated with this issue, bounds on the maximum number of bicliques were given. In this paper we study bounds on the minimun number of bicliques of a graph. Since adding false-twin vertices to $G$ does not change the number of bicliques, we restrict to false-twin-free graphs. We give a tight lower bound on the minimum number bicliques for a subclass of $\{C_4$,false-twin$\}$-free graphs and for the class of $\{K_3$,false-twin$\}$-free graphs. Finally we discuss the problem for general graphs.Comment: 16 pages, 4 figue

Vertex removal in biclique graphs

A \textit{biclique} is a maximal bipartite complete induced subgraph. The \textit{biclique graph} of a graph $H$, denoted by $KB(H)$, is the intersection graph of the family of all bicliques of $H$. In this work we address the following question: Given a biclique graph $G=KB(H)$, is it possible to remove a vertex $\beta$ of $G$, such that $G - \{\beta\}$ is a biclique graph? And if possible, can we obtain a graph $H'$ such that $G - \{\beta\} = KB(H')$? We show that the general question has a ``no'' for answer. However, we prove that if $G$ has a vertex $\beta$ such that $d(\beta) = 2$, then $G-\{\beta\}$ is a biclique graph and we show how to obtain $H'$

Proper Hamiltonian Cycles in Edge-Colored Multigraphs

A $c$-edge-colored multigraph has each edge colored with one of the $c$ available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges have the same color. In this work we establish sufficient conditions for a multigraph to have a proper Hamiltonian cycle, depending on several parameters such as the number of edges and the rainbow degree.Comment: 13 page

Dynamic Secondary Electron Emission in Rough Composite Materials

The interaction of ionizing radiation with matter is of critical importance in numerous areas of science and technology like space and vacuum technology and even medicine and biotechnology. Secondary electron emission is a consequence of electron irradiation on materials. We achieve extremely low secondary electron emission yield values smaller than 0.2, even up to incident electron energies ~1 keV, due to an undocumented synergy between neighbouring metal and dielectric domains in composite samples. To investigate this experimental discovery, we propose a simple 3D model where the dielectric and metallic domains are arranged in parallel and interleaved. The proposed surface profile has a triangular shape to model the surface roughness. We obtain a continuous equation to describe the electric field that arises between grounded conductors and charged dielectrics domains. The calculated trajectories of secondary electrons in this 3D geometry are used to predict dynamic secondary emission yield, which strongly depends on the charge accumulated in the dielectric domains. This research paves the way to design new materials of low secondary emission yield, addressing the technological problem not yet resolved to inhibit the electron avalanche in RF equipment that limit their maximum working power

Dynamic secondary electron emission in dielectric/conductor mixed

Secondary Emission Yield (SEY) of dielectric materials is of great importance for prediction and testing of the Multipaction discharge in RF components for space applications. An atypical behavior of the SEY of coatings composed by a mixture of conductor and dielectric microparticles was reported and modeled in [1]; in this original model, the interactions between dielectric and conductor particles were not taken into account, but an effective action of the surface voltage generated within the sample was included. The aim of the present contribution is to more accurately model the effect the electric fields between dielectric and conductor particles have on secondary electrons emitted by the sample. One of the most prominent features of the coatings is their roughness, so a model is proposed here that takes into account both the roughness and the charging of the dielectric particles to explain the unusual charging behavior of these coatings

SUGERENCIAS PARA PERFECCIONAR EL TRABAJO CULTURAL COMUNITARIO DE LA ESCUELA PRIMARIA RURAL

El presente tiene como objetivo ofrecer sugerencias para perfeccionar el trabajo cultural comunitario en la escuela primaria Manuel Angulo Farrán, en la comunidad rural de La Victoria. Los resultados fundamentales se aprecian en la gestión cultural comunitaria de la escuela primaria rural, la producción y consumo de bienes culturales y espirituales, la participación en la construcción y defensa de la cultura, y la preservación del patrimonio cultural. ABSTRACT This article has as objective to offer suggestions to improve the cultural work in the primary school Manuel Angulo Farrán, in a rural community of La Victoria. The main results can be seen in the communitarian and cultural commitment of primary rural school, production and consume of cultural and spiritual goods, the participation in the construction and defense of culture as well as the preservation of cultural patrimony. KEY WORDS: culture, rural community, primary school, cultural work

Extremely low secondary electron emission from metal/dielectric particulate coatings

Research on low secondary electron emission coatings is essential for the design and manufacture of space high-power RF devices without multipactor discharge. This paper discusses some of the factors that reduce secondary electron emission for metal-dielectric surfaces. We have studied the total electron yield (TEY) behavior of a particulate coating composed of a mixture of a metal (aluminum) nanoparticulates in solid state contact with a particulate dielectric material (polyimide thermosetting resin). Surface charging, roughness, and volume fraction are utilized as the main parameters to characterize the electron emission behavior, which can effectively be determined by continuous (total dose 42.5 nC/mm2) and pulsed (1,1 fC/mm2/pulse) electron irradiation methods. Apart from the important role played by surface composition in the TEY, the influence of the dielectric volume fraction has demonstrated to be critical to achieve a significant reduction of TEY. Analytical surface techniques such as field emission scanning microscopy and X-ray photoelectron spectroscopy were used, because they are very effective in providing insight into the effect of charging on the surface. Typical TEY parameters of the aluminum foil exposed to the air are: the first crossover energy, E1=20 eV, TEY maximum, σmax = 2.9, and Emax = XXX eV; these contrast with the dielectric values: E1= 30 eV, σmax = 2.5, and Emax = XXX eV. However, it was found that E1 of the particulate sample increased with increasing dielectric volume fraction. An extremely high first crossover energy, E1\u3e1000eV, was obtained after the gold metallization of the metal/dielectric coatings of 0.75 volume fraction. It is also remarkable that TEY was 0.2 for E\u3c1000\u3eeV, the low energy emitted electrons appear to be reabsorbed. Another remarkable fact is that TEY curves measured by using either the continuous or the pulsed methods overlap in the whole primary energy range, dissipate the much larger electron dose of the continuous method as compared to the very low dose of the pulsed method; this result is usually understood as an indication of minimal influence of charging on TEY