Dirac's minimum degree condition restricted to claws

Let G be a graph on n 3 vertices. Dirac's minimum degree condition is the condition that all vertices of G have degree at least . This is a well-known sufficient condition for the existence of a Hamilton cycle in G. We give related sufficiency conditions for the existence of a Hamilton cycle or a perfect matching involving a restriction of Dirac's minimum degree condition to certain subsets of the vertices. For this purpose we define G to be 1-heavy (2-heavy) if at least one (two) of the end vertices of each induced subgraph of G isomorphic to K1,3 (a claw) has (have) degree at least . Thus, every claw-free graph is 2-heavy, and every 2-heavy graph is 1-heavy. We show that a 1-heavy or a 2-heavy graph G has a Hamilton cycle or a perfect matching if we impose certain additional conditions on G involving numbers of common neighbours, (local) connectivity, and forbidden induced subgraphs. These results generalize or extend previous work of Broersma & Veldman, Dirac, Fan, Faudree et al., Goodman & Hedetniemi, Las Vergnas, Oberly & Sumner, Ore, Shi, and Sumner

Nihilism Inc.: Environmental Destruction and the Metaphysics of Sustainability

The spectre of global environmental destruction is before us, the legacy of the expansion and domination of the world by European civilization. Not even the threat to the continued existence of humanity is enough to move the members of this civilization to alter its trajectory. And Marxism, which had held out the possibility of creating a new social order, has been swept from the historical stage by the failure of Eastern European communism. Nihilism Inc. is an attempt to overcome this crisis. Examining the relationship between metaphysical assumptions, ideas, social practices, institutions and economic processes in the formation and evolution of European civilization, it offers a genealogy of its current nihilism. The theory and practice of Marxism are analysed to show why the Soviet Union proved even more environmentally destructive and even less responsive to the environmental crisis than the West. These analyses reveal the need for a radical cultural transformation, a transformation which can only be effected on the foundation of a new metaphysics. The final part of this work offers the required metaphysics, clearing the way for the creation of an environmentally sustainable civilization

Amrit Singh and the Birmingham Quean: fictions, fakes and forgeries in a vernacular counterculture

For a literary critic preparing a scholarly edition of a text like this within an epistème that disparages the theory underpinning it for being tainted with the gestural idealism of 1968 and the neon-glare of 1980s high postmodernism, the crucial question is how to reconcile the commitment to authenticity ingrained in historicist textual studies (perhaps the critic’s only viable disciplinary inheritance) with the author’s implicit antagonism to any such quietist approach. The encounter inevitably becomes a battle of wills. In the course of the current project, this theoretical struggle escalates exponentially as doubts concerning the authenticity (and indeed the existence) of both writer and manuscript are multiplied. If a thesis can be retrospectively extrapolated from this project, it is the argument that fiction is demonstrably a tractable forum for research in the Arts and Social Sciences: all the more tractable for its anti-authenticity. The critic’s loss is the novelist’s gain. Specifically, in this case, the faithful historian of late twentieth century literatures, languages and cultures can solve the key dilemma of the subject by working under the auspices of Creative Writing. Only in this way can justice be done to the most cogent intellectual trend of the posmodern period (perhaps its defining feature): one that revelled in its own pluralities, ambiguities and contradictions, and resisted all the unifying, teleological models of ‘history’ that had been implicated in the century’s terrible ‘final solutions’. In other words, only fiction can tell the history of a culture that rejects that history. If this means condoning forgery… so be it

Beyond European Civilization: Marxism, Process Philosophy, and the Environment

Beyond European Civilization is the sequel to Nihilism Incorporated, a work in which I described how European civilization came to embody a nihilistic world-orientation and to conquer the world, and how, through the expansion of capitalism, it continues to impose its environmentally destructive culture on the rest of humanity. Through a critical analysis of the failure of Marxism to overcome the defects of European culture, Beyond European Civilization elaborates the foundations for a culture to transcend European civilization