On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

Coloring Algorithms on Subcubic Graphs

We present efficient algorithms for three coloring problems on subcubic graphs (ones with maximum degree 3). These algorithms are based on a simple decomposition principle for subcubic graphs. The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring

Prescription Narratives: Re-reading Joseph Cornell’s Pharmacy Series as Modernist Anti-dote

‘The Apothecary’s Chest: Magic, Art and Medication’ was a one-day symposium held at the University of Glasgow on November 24, 2007. The symposium called for a discussion on the evolution of the notions of mysticism, knowledge and superstition in the way they are intertwined in both science and the literary imagination in the figure of healers such as the apothecary, the alchemist, the shaman. There were three main areas of interest. The first involved traditional perceptions of physicians, who combined knowledge and superstition and thus bordered, in their practices, on the sphere of the occult. The second theme, evolving from the first, proposed an inquiry of the overlapping interests and processes of science, magic and prophesy, as well as of the implications and consequences of a privileged access to medical knowledge, while the third subject of discussion concentrated on the development of the symbolism of the healer in literature, history, philosophy of science, anthropology, theology, film and art. The twelve papers included in this volume, papers presented by doctoral candidates and young scholars from across a range of geographical regions and disciplines, result in a collection of approaches to an investigative field with topics ranging from mystical traits of mundane materials to the origins of the occult and gender struggles. The thirteenth and final essay included in the volume, Professor Bill Herbert’s ‘From Mere Bellies to the Bad Shaman’, is an exploration of the modern role of the contemporary poet in the form of an extended conversation initiated at the closing of the conference, when Professor Herbert was asked to combine a poetry reading with a few observations on the relationship between the poet and the shaman