Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Global Geographic Distribution and Host Range of Fusarium circinatum, the Causal Agent of Pine Pitch Canker

Fusarium circinatum, the causal agent of pine pitch canker (PPC), is currently one of the most important threats of Pinus spp. globally. This pathogen is known in many pine-growing regions, including natural and planted forests, and can affect all life stages of trees, from emerging seedlings to mature trees. Despite the importance of PPC, the global distribution of F. circinatum is poorly documented, and this problem is also true of the hosts within countries that are affected. The aim of this study was to review the global distribution of F. circinatum, with a particular focus on Europe. We considered (1) the current and historical pathogen records, both positive and negative, based on confirmed reports from Europe and globally; (2) the genetic diversity and population structure of the pathogen; (3) the current distribution of PPC in Europe, comparing published models of predicted disease distribution; and (4) host susceptibility by reviewing literature and generating a comprehensive list of known hosts for the fungus. These data were collated from 41 countries and used to compile a specially constructed geo-database. A review of 6297 observation records showed that F. circinatum and the symptoms it causes on conifers occurred in 14 countries, including four in Europe, and is absent in 28 countries. Field observations and experimental data from 138 host species revealed 106 susceptible host species including 85 Pinus species, 6 non-pine tree species and 15 grass and herb species. Our data confirm that susceptibility to F. circinatum varies between different host species, tree ages and environmental characteristics. Knowledge on the geographic distribution, host range and the relative susceptibility of different hosts is essential for disease management, mitigation and containment strategies. The findings reported in this review will support countries that are currently free of F. circinatum in implementing effective procedures and restrictions and prevent further spread of the pathogen

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter thickness. By restricting the edges to be straight, we obtain the geometric thickness. By additionally restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth k, the maximum thickness and the maximum geometric thickness both equal ⌈k/2⌉. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth k, the maximum book thickness equals k if k ≤ 2 and equals k + 1 if k ≥ 3. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215–221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity

Persons With Multiple Sclerosis Show Altered Joint Kinetics During Walking After Participating in Elliptical Exercise

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'Have you seen Bloomberg?': satellite news channels as agents of the new visibility

With the proliferation of transnational television flows, viewers can see their national affairs, traditionally covered predominantly by national news, portrayed by cross-border news channels. This article examines how transnational satellite news coverage of national events enhances nations' global visibility, and influences national public debate over national narratives. An analysis of the public debates in Spain and France over transnational channels' coverage of the March 2004 terror bombings in Madrid and the October 2005 French riots, respectively, provides the basis for discussing the implications of the `new visibility' (Thompson, 2005) of nations, in today's media age. The analysis demonstrates how transnational networks' coverage of these events generated estrangement, de-familiarized and cast doubt on national narratives and commonsensical discourses of us/them, thereby offering viewers an alternative distance from their national unit and encouraging a self-reflexive process of introspection and critical discussion. This process may open up the possibility for a more inclusive national space and strengthen democratic culture, but at the same time it triggers instabilities, which might contribute to citizens' loss of trust in the news media — a dangerous scenario for democracy