The metric dimension and metric independence of a graph

A vertex x of a graph G resolves two vertices u and v of G if the distance from x to u does not equal the distance from x to v. A set S of vertices of G is a resolving set for G if every two distinct vertices of G are resolved by some vertex of S. The minimum cardinality of a resolving set for G is called the metric dimension of G. The problem of nding the metric dimension of a graph is formulated as an integer pro- gramming problem. It is shown how a relaxation of this problem leads to a linear programming problem and hence to a fractional version of the metric dimension of a graph. The linear programming dual of this problem is considered and the solution to the corresponding integer programming problem is called the metric independence of the graph. It is shown that the problem of deciding whether, for a given graph G, the metric dimension of G equals its metric independence is NP- complete. Trees with equal metric dimension and metric independence are characterized. The metric independence number is established for various classes of graphs.Preprin

Re-conceptualising sustainable development on the basis of the capability approach: A model and its difficulties

This paper sketches a re-conceptualisation of sustainable development (SD) on the basis of the capability approach (CA). The notion sustainable development was developed as a compromise in a political process and has been re-interpreted (some say: diluted) again and again in the last 20 years. When modelling the notion through the lenses of the capability approach, difficulties occur that are at the core of SD and of CA or that are due to their combination. Our paper shows why it is not that easy to replace needs in the Brundtland definition of SD with capabilities. In our model, the differences between systemic and individual levels become clear and herewith the necessity to include both when dealing with issues of SD. The most salient difficulties relate to the multidimensionality and dynamics on both levels. Confronted to these difficulties, demanding individuals to consciously choose sustainable actions seems to be heroic. We propose two ways to alleviate the cognitive and moral burden on individuals by concentrating on the natural environment and by introducing collective institutions. Both alleviations are far from evident, though; this concerns their justification as well as their operationalization. --capability approach,sustainable development,systemic level,collective institutions,dynamics

Global cycle properties in graphs with large minimum clustering coefficient

The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete structural characterization of those locally connected graphs, with minimum clustering coefficient 1/2 and maximum degree at most 6, that are fully cycle extendable is given in terms of strongly induced subgraphs with given attachment sets. Moreover, it is shown that all locally connected graphs with minimum clustering coefficient 1/2 and maximum degree at most 6 are weakly pancyclic, thereby proving Ryjacek's conjecture for this class of locally connected graphs.Comment: 16 pages, two figure

Die Macht der OhnMächtigen : über Konversionen der Leidenschaft beim Spiel im Spiel und die Rolle des Regietheaters ; Vortrag im Rahmen der Salzburger Festspieldialoge am 12. August 2009

Mit dem Motto »Das Spiel der Mächtigen« haben die Salzburger Festspieldialoge 2009 einen Titel aufgegriffen, den ursprünglich Giorgio Strehler für seine Inszenierung von William Shakespeares Königsdramen gewählt hatte, die 1973 bei den Salzburger Festspielen gezeigt wurde. Der Titel steht aber nicht nur für eine groß angelegte Shakespeare-Inszenierung, sondern geradezu programmatisch auch für eine Form des Regietheaters, die in Salzburg Furore machte. Denn Strehler nahm bei den Stücken Heinrich V. und Heinrich VI. nach eigenen dramaturgischen Erwägungen Kürzungen vor, komponierte sie um und kommentierte sie durch andere Dramen Shakespeares, indem er Textpassagen aus Macbeth, König Lear, König Johann und Richard II. in seine Inszenierung integrierte

Lulu oder die Last mit der Lust : "Die Urgestalt des Weibes" – ein Männertrauma

Der Vorhang öffnet sich zunächst nur einen Spalt zu Alban Bergs Oper Lulu, die anlässlich der Salzburger Festspiele 2010 in der Felsenreitschule inszeniert wurde. Zu erwarten ist, dass nun ein Sänger in der Rolle des Tierbändigers mit Hetzpeitsche in der einen und Revolver in der anderen Hand aus dem bunt gestreiften Vorhang wie durch den Eingang eines Zirkuszeltes schlüpft, um anzukündigen, dass in der nun folgenden Aufführung nicht – wie in gängigen "Lust und Trauerspielen" – lediglich gezähmte "Haustiere" gezeigt werden, sondern hier "[m]it heißer Wollust und mit kaltem Grauen" endlich "[d]as wahre Tier, das wilde, schöne Tier" erlebt werden kann

The capability approach to intergenerational justice: A survey

The politically influential idea of sustainable development is closely tied to the concept of inter- and intragenerational justice without clarifying these concepts and their relationship. In developing an account of human development, the capability approach conceptualizes parts of intragenerational justice, but not intergenerational justice. After explaining briefly our motivation by establishing the link to sustainable development, this paper aims to close the gap in two steps: first, it clarifies elements of a universal theory of justice. Second, it examines how well the CA can take up these elements before drafting how this would translate back to the political context of sustainable development. --