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A.-L. Daniau, P. J. Bartlein, S. P. Harrison, I. C. Prentice, S. Brewer, P. Friedlingstein, T. I. Harrison-Prentice, J. Inoue, K. Izumi, J. R. Marlon, S. Mooney, M. J. Power, J. Stevenson, W. Tinner, M. Andrič, J. Atanassova, H. Behling,M. Black, O. Blarquez, K. J. Brown, C. Carcaillet, E. A. Colhoun, D. Colombaroli, B. A. S. Davis, D. D’Costa, J. Dodson,(More)
The Kneser graph Kn:k for positive integers n ≥ k has as its vertex set the k-element subsets of some n-set, with disjoint sets being adjacent. Every finite simple graph can be found as an induced subgraph of some Kneser graph; this can be viewed as a way of representing graphs by labelling their vertices with sets. We explore questions of finding the(More)
OBJECTIVE To evaluate clinical and cost effectiveness of implementing evidence-based guidelines for the prevention of stroke. DESIGN Cluster-randomised trial SETTING Three primary care organisations in the North of England covering a population of 400,000. PARTICIPANTS Seventy six primary care teams in four clusters: North, South & West, City I and(More)
A function f : V (G) → {0, 1, 2} is a Roman dominating function if for every vertex with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. We introduce two fractional Roman domination parameters, γR ◦ f and γRf , from relaxations of two equivalent integer programming formulations of Roman domination (the former using open neighborhoods and the later(More)
  • Matt Walsh
  • Discussiones Mathematicae Graph Theory
  • 2007
Mynhardt has conjectured that if G is a graph such that γ(G) = γ(πG) for all generalized prisms πG then G is edgeless. The fractional analogue of this conjecture is established and proved by showing that, if G is a graph with edges, then γf (G×K2) > γf (G).
Economic studies on simulated natural gas hydrate reservoirs have been compiled to estimate the price of natural gas that may lead to economically viable production from the most promising gas hydrate accumulations. As a first estimate, large-scale production of natural gas from North American arctic region Class 1 and Class 2 hydrate deposits will be(More)
Given a combinatorial designD with block set B, its traditional block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and only if b1 and b2 have non-empty intersection. In this paper we consider the S-block-intersection graph, in which two vertices b1 and b2 are adjacent if and only if |b1 ∩ b2| ∈ S.(More)
Let G be a finite simple graph of order n, maximum degree ∆, and minimum degree δ. A compact regularization of G is a ∆-regular graph H of which G is an induced subgraph: H is symmetric if every automorphism of G can be extended to an automorphism of H. The index |H : G| of a regularization H of G is the ratio |V (H)|/|V (G)|. Let mcr(G) denote the index of(More)
when opposing forces are aligned. Whether it be tectonic plates pushing against each other, religious sects debating ideology, or two suitors trying to impress the same girl, the tension builds. However, as this tension mounts, something else happens as well: Potential energy is created. The more these forces push against each other, the more potential(More)