Protecting a Graph with Mobile Guards

Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been proposed. In this survey we describe a number of these models with particular attention to the case when the attack sequence is infinitely long and the guards must induce some particular configuration before each attack, such as a dominating set or a vertex cover. Results from the literature concerning the number of guards needed to successfully defend a graph in each of these problems are surveyed.Comment: 29 pages, two figures, surve

Total domination stable graphs upon edge addition

AbstractA set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination edge addition stable if the addition of an arbitrary edge has no effect on the total domination number. In this paper, we characterize total domination edge addition stable graphs. We determine a sharp upper bound on the total domination number of total domination edge addition stable graphs, and we determine which combinations of order and total domination number are attainable. We finish this work with an investigation of claw-free total domination edge addition stable graphs

Graph critical with respect to variants of Domination

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The random geometry of equilibrium phases

This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6. Random-cluster representations 7. Uniqueness and exponential mixing from non-percolation 8. Phase transition and percolation 9. Random interactions 10. Continuum modelsComment: 118 pages. Addresses: [email protected] http://www.mathematik.uni-muenchen.de/~georgii.html [email protected] http://www.math.chalmers.se/~olleh [email protected]

The status of ecophilosophy and the ideology of nature.

Ecophilosophy is an attempt to render a new philosophy of nature, generated by the need to liberate nature from the inherently domineering disposition of humankind. Although I am sympathetic to this effort, I believe that the current ambiguity of its content (who or what is to survive) carries with it the potentiality for new forms of oppression. I argue that ecophilosophy suffers from a kind of Habermasian self-deception, taking on a vague concept of nature that deceptively appears to do the philosophical work of healing the epistemological gap between nature and humans. My reconstruction unifies this loosely-defined vision along the lines of an equivocal use of two key concepts, the domination of nature and nature itself, revealing the potentially subversive character of its implicitly universalist philosophy of nature. Ecophilosophers, rather than distinguishing themselves, fail to improve upon Francis Bacon\u27s suggestion that attention to nature will liberate us. Their satisfaction with ecological solutions indicates that they miss the essential ideological consequence of the modern project: the domination by some humans over others has been covered over by a self-deceptive belief in the liberating character of scientific methodology. By arguing for the emancipatory capacity of ecology, they get themselves into a Marcusian-like bind, advocating this new science while at the same time rejecting scientific rationality as a pivotal component of their notion of the domination of nature. Because of this they are forced to argue that ecology is qualitatively different, offering a new kind of rationality that contains the necessary ingredients for radically changing society. Ecophilosophers must reconsider the epistemologically naive and ideologically negative repercussions of this position as I demonstrate with an analysis of the potentially repressive relationships that exist between fourth world cultures and the environmental community. I conclude by subjecting the Habermasian, universalist framework to revision as indicated by the possibilities of a new eco-vision, emerging from the contextual episteme of a reworked ecofeminist perspective

Distances and Domination in Graphs

This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present

From rubber bands to rational maps: A research report

This research report outlines work, partially joint with Jeremy Kahn and Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal surfaces with boundary. One one hand, this lets us tell when one rubber band network is looser than another, and on the other hand tell when one conformal surface embeds in another. We apply this to give a new characterization of hyperbolic critically finite rational maps among branched self-coverings of the sphere, by a positive criterion: a branched covering is equivalent to a hyperbolic rational map if and only if there is an elastic graph with a particular "self-embedding" property. This complements the earlier negative criterion of W. Thurston.Comment: 52 pages, numerous figures. v2: New example

Natural Selection and the Origin of Economic Growth

This research develops an evolutionary growth theory that captures the interplay between the evolution of mankind and economic growth since the emergence of the human species. This uni...ted theory encompasses the observed evolution of population, technology and income per capita in the long transition from an epoch of Malthusian stagnation to sustained economic growth. The theory suggests that prolonged economic stagnation prior to the transition to sustained growth stimulated natural selection that shaped the evolution of the human species, whereas the evolution of the human species was the origin of the tak-o from an epoch of stagnation to sustained growth.Growth; Technological Progress; Fertility; Human Capital; Evolution; Natural Selection; Malthusian Stagnation