Exact colorations of graphs and digraphs

A coloration is an exact regular coloration if whenever two vertices are colored the same they have identically colored neighborhoods. For example, if one of the two vertices that are colored the same is connected to three yellow vertices, two white and red, then the other vertex is as well. Exact regular colorations have been discussed informally in the social network literature. However they have been part of the mathematical literature for some time, though in a different format. We explore this concept in terms of social networks and illustrate some important results taken from the mathematical literature. In addition we show how the concept can be extended to ecological and perfect colorations, and discuss how the CATREGE algorithm can be extended to find the maximal exact regular coloration of a graph.

A generational scheme for partitioning graphs

Graph partitioning divides a graph into several pieces by cutting edges. Very effective heuristic partitioning algorithms have been developed which run in real-time, but it is unknown how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. Distinctive features are the transmission and modification of whole subdomains (the partitioned units) that act as genes, and the use of a multilevel heuristic algorithm to effect the crossover and mutations. Its effectiveness is demonstrated by improvements on previously established benchmarks.

On Hamilton cycles in locally connected graphs with vertex degree constraints

It is shown that every connected, locally connected graph with the maximum vertex degree Δ(G)=5 and the minimum vertex degree δ(G)3 is fully cycle extendable. For Δ(G)4, all connected, locally connected graphs, including infinite ones, are explicitly described. The Hamilton Cycle problem for locally connected graphs with Δ(G)7 is shown to be NP-complete

Coursework uploads and zero-tolerance deadlines

Clear assessment deadlines and severe penalties for late submission of coursework are a feature of a number of UK universities. This presents a severe challenge for any online upload system. Evidence from a range of different implementations at the School of Computing and Mathematical Sciences at the University of Greenwich over the past few years is examined to assess the impact of a zero-tolerance deadline policy on the way students work and the problems that arise. Suggestions are made on how to minimise any possible negative impact of a zero-tolerance deadline policy on the administration of the system and on staff and students.

To tremble the zero: art in the age of algorithmic reproduction

'To Tremble the Zero: Art in the Age of Algorithmic Reproduction' is a philosophic, political and sensuous journey playing with (and against) Benjamin's 'Art in the Age of Mechanical Reproduction'. In an age inundated by the 'post-': postmodernity, posthuman, post art, postsexual, post-feminist, post-society, post-nation, etc, 'To Tremble the Zero' sets out to re/present the nature of what it means to do or make 'art', as well as what it means to be or have 'human/ity' when the ground is nothing other than the fractal, and algorithmically infinite, combinations of zero and one. The work will address also the unfortunate way in which modern forms of metaphysics continue to creep 'unsuspectingly' into our understanding of contemporary media/electronic arts, despite (or perhaps even because of) the attempts by Latour, Badiou, or Agamben especially when addressing the zero/one as if a contradictory 'binary' rather than as a kind of 'slice' or (to use Deleuze and Guattari) an immanent plane of immanence. This work argues that by retrieving Benjamin, Einstein, Gödel, and Haraway, a rather different story of art can be told.