On the size of identifying codes in triangle-free graphs

In an undirected graph $G$, a subset $C\subseteq V(G)$ such that $C$ is a dominating set of $G$, and each vertex in $V(G)$ is dominated by a distinct subset of vertices from $C$, is called an identifying code of $G$. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph $G$, let \M(G) be the minimum cardinality of an identifying code in $G$. In this paper, we show that for any connected identifiable triangle-free graph $G$ on $n$ vertices having maximum degree $\Delta\geq 3$, \M(G)\le n-\tfrac{n}{\Delta+o(\Delta)}. This bound is asymptotically tight up to constants due to various classes of graphs including $(\Delta-1)$-ary trees, which are known to have their minimum identifying code of size $n-\tfrac{n}{\Delta-1+o(1)}$. We also provide improved bounds for restricted subfamilies of triangle-free graphs, and conjecture that there exists some constant $c$ such that the bound \M(G)\le n-\tfrac{n}{\Delta}+c holds for any nontrivial connected identifiable graph $G$

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Decken- und Wandmalerei in Sachsen

Die Broschüre des Landesamtes ist mit der Decken- und Wandmalerei einer besonderen Kunstform gewidmet und stellt Betreuungsaufgaben des Referates Restaurierung vor. Außergewöhnliche Beispiele aus acht Jahrhunderten werden vorgestellt, die teils während Baumaßnahmen entdeckt, gesichert, gerettet, erforscht und restauriert werden konnten. Sie stehen für die Vielfalt in Sachsen, sowohl kunsttechnologisch als auch thematisch. Genauso vielfältig sind die Gebäude, in denen Wand- und Deckenmalereien zu finden sind – und zwar auf dem gesamten Territorium des Freistaats. Die Ausstellung bietet neben Bekanntem auch Überraschungen in eher unscheinbaren Bauten – wer erwartet schon in einem Kindergarten ein Werk Conrad Felixmüllers? Wandmalereien gelten als stets gefährdet, sind sie doch unmittelbar mit dem Mauerwerk verbunden und den Umwelteinflüssen direkt ausgesetzt. Das Spannungsfeld bei der Erhaltung von Wandmalereien zeigen die ausgewählten Beispiele auf. Redaktionsschluss: 15.10.202

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

A multipurpose experimental facility for advanced X-ray Spectrometry applications

Ponencia presentada en la European Conference on X-Ray Spectrometry (EXRS). 2014Motivation, Ultra High Vacuum Chamber (UHVC) project: To support/enhance the training of scientists/engineers from developing countries in the operation of synchrotron radiation instrumentation; To provide beam time access for R&D projects and hands-on training in SR-XRS based techniques; To promote networking and knowledge sharing; To increase the quality and the competitiveness of the developing countries to apply beam time proposals at SR facilities; To contribute in the further development of XRS techniques in applications with socioeconomicalrelevance (characterization of energy storage/conversion materials, environmental, biological and biomedical applications)Fil: Leani, Juan José. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Leani, Juan José. Nuclear Science and Instrumentation Laboratory, IAEA Laboratories; Austria.Física Atómica, Molecular y Química (física de átomos y moléculas incluyendo colisión, interacción con radiación, resonancia magnética, Moessbauer Efecto.

A Class of Three-Colorable Triangle-Free Graphs

The chromatic number of a triangle-free graph can be arbitrarily large. In this article, we show that if all subdivisions of K2, 3 are also excluded as induced subgraphs, then the chromatic number becomes bounded by 3. We give a structural characterization of this class of graphs, from which we derive an coloring algorithm, where n denotes the number of vertices and m the number of edges of the input graph