Various results on the toughness of graphs

Let G be a graph, and let t 0 be a real number. Then G is t-tough if t!(G − S) jSj for all S V (G) with !(G − S) > 1, where !(G − S) denotes the number of components of G − S. The toughness of G, denoted by (G), is the maximum value of t for which G is t-tough (taking (Kn) = 1 for all n 1). G is minimally t-tough if (G) = t and (H) < t for every proper spanning subgraph H of G. We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sucient (degree) conditions implying (G) t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares

Stop de nieuwe schoolstrijd

Het debat over het onderwijs in ons land dreigt danig uit de hand te lopen. Dat komt vooral doordat de deelnemers er nogal ideologisch geladen standpunten op nahouden. Aan de ene kant staan fervente vernieuwers uit de hoek van het ‘Nieuwe Leren’. Zij claimen het gelijk van de zeepfabrikant: het product is beter omdat het nieuw is. Aan de andere kant beweegt zich een snel groeiende groep conservatieven, inmiddels verzameld in de belangenvereniging ‘Beter Onderwijs Nederland’. Hun motto lijkt rechtstreeks ontleend aan Bordewijks klassieker Bint: onderwijs is kennis stampen en dat vereist nu eenmaal tucht, geen nieuwlichterij

Long D3-cycles in graphs with large minimum degree

It is shown that if G is a 2-connected graph on n vertices, with minimum degree such that n≤4δ−6, and with a maximum independent set of cardinality , then G contains a cycle of length at least min {n,n+2δ−2α−2g or G ε F, where F denotes a well-known class of nonhamiltonian graphs of connectivity 2

Forbidden subgraphs that imply Hamiltonian-connectedness

It is proven that if $G$ is a $3$-connected claw-free graph which is also $Z_3$-free (where $Z_3$ is a triangle with a path of length $3$ attached), $P_6$-free (where $P_6$ is a path with $6$ vertices) or $H_1$-free (where $H_1$ consists of two disjoint triangles connected by an edge), then $G$ is Hamiltonian-connected. Also, examples will be described that determine a finite family of graphs $\cal{L}$ such that if a 3-connected graph being claw-free and $L$-free implies $G$ is Hamiltonian-connected, then $L\in\cal{L}$. \u

The rise of new knowledge types and their trailblazers, and the management of value chains

In this article, the authors argue that there is no such thing as the knowledge society. Like many others authors, they claim that the fundamental transformations of our time can be typified as the end of the national ‘industrial society’ and the move towards some kind of global society dominated by the production and use of knowledge. They argue, however, that these transformations not necessarily produce a convergence of national and regional socio-economic structures. In industrial society two types of knowledge were dominant: ‘technical knowledge’ and ‘social knowledge’. In our time, the growing diverseness of individual and group identities produced by reflexivisation, globalisation and the advancement of information technologies calls for the development and application of a new type of knowledge: ‘cultural knowledge’. They analyse the consequences of the increased significance of cultural knowledge in the economic sphere in terms of the division of labour, and subsequently conceptualise three different types of knowledge societies: ‘the techno-cultural’, ‘the socio-cultural’ and the ‘socio-technical knowledge society’. Finally, they will portray three ‘categories’ of trailblazers of the knowledge societies, new professionals that perform ‘meta business functions’. These trailblazers directly or indirectly create new value chains by linking or destroying existing ones, and breaking up others in to pieces in order to create new combinations. These professionals, in other words, actively manage value chains